I just happened to have recently written a little paper on the spoke length formula, so with my knowledge about wheels refreshed, I think I'll take a shot at answering this question. Let me approach it in parts.
Radial Versus Tangential
As noted by other answers already, the primary advantages are a slightly shortened spoke length and ease of wheelbuilding. I think the numerous disadvantages far outweigh these factors though. You have a pretty good understanding of how tangentially-spoked wheels respond to various inputs, so I won't elaborate there unless you want me to.
By how much are the spokes shortened, one might ask? Not that much at all. For reference, here's the spoke length formula (my work):
As you can see, the crossing number c is only present inside the argument of the cosine function. The term attached to the cosine function is fairly small because its coefficient (twice the product of the rim radius and hub radius) is small by itself compared to the square of the rim radius. By substituting the arbitrary values of rim radius Rr = 300mm, hub radius Rh = 30mm, hub flange offset ho = 50mm, and spoke count s = 32, we get a length of 294.1mm for a 3-cross wheel, and 274.6mm for a radially-spoked one. The difference in length is 19.5mm, which translates to a mass difference of approximately 15.5g for 2mm round stainless steel spokes. Nice.
And as for air drag? Here's the idealistic drag equation (screenshotted from Google):
What we are concerned about here is A, the cross-sectional area. Everything else is a constant if we are comparing two otherwise identical spokes of different lengths. Using the simplification of spokes intersecting the airstream perpendicularly (so velocity is constant), I calculate a reduction of cross-sectional area of 6.5% from an already insignificant value. Nice.
Evidently, this point is fairly moot.
I don't think the time savings is particularly important either. It doesn't take that long to spoke either style of wheel; the primary time expenditure is on tensioning and trueing.
Your other two questions on the other SE websites.
On the Engineering SE, you asked:
How can wheels with spokes concurrent at the center be solid?
I think you know the answer to this question already: no real-life item is perfectly stiff. Since you correctly mention that spokes have negligible lateral stiffness, a radially-built bicycle wheel is indeed going to suffer when considering twists of the hub relative to the rim. We see that a tangent line to the hub flange drawn where any spoke meets it is in fact perpendicular to the spoke, so the spoke is unable to handle lateral loads. In order for a spoke to provide/resist a torque at the hub, it must deflect to change the spoke-hub angle. Unfortunately, for this to happen, the spoke must lengthen to a great extent as the hypotenuse grows, enough to break it if non-trivial torque is applied.
You then note,
Of course a bicycle wheel is so light precisely because it is not a solid object, but the rim and hub have no relative "wobble".
I think this is a slightly skewed way of looking at it. The reason a wire-spoked wheel is so lightweight for its load capacity is that material is only present where its needed, and this material is being used only in its "best", most efficient directions. The rim and hub are relatively stable because there are many forces of large magnitude (spoke tension) acting on the pair which hold them in their most stable position relative to one another.
Virtually the same question is asked on the Physics SE website.
Let me now address your five main points:
The tension in radial spokes ought to be considerably higher than on tangent spokes in a traditional arrangement. The spokes on radially spoked wheels seem considerably thicker, and this suggests that an increased tension is expected. A much higher tension also means that the "activation" angle is far smaller, leading to a more solid wheel.
I must begin by noting I have no first-hand experience with radial wheels. That said, I don't think there will be any significant tension difference; for starters, I don't tension my 2× versus 3× wheels any differently. This is confirmed by Park Tool's conversion table for use with their tension meter: there is no separate category for radial lacing.
I think a lot of radially-spoked wheels use aerodynamic bladed spokes, so they may appear thicker when viewed from the side. Furthermore, note that spoke thickness is largely independent of expected tension. It is common practice to use purposefully thinner spokes (eg. Juhist's beloved DT Swiss Alpine III) to make the spokes stretch more for the same tension, giving a more evenly tensioned wheel.
Likewise, given the "activation rotation", we would expect a radially laced wheel to be "mushy" under torque. This would be an advantage, acting like a shock absorber.
I think any significant mushiness would be immediately followed by catastrophic wheel failure as the spokes elongate past their breaking point. When you accelerate the bike, the wheels are expected to spin . Hence, even if there is, say, 10° of mushiness, the wheel is going to be rotating several full turns (several thousand degrees of rotation) very shortly.
Even if this effect were real and significant, it would certainly not act like a shock absorber, at least not in a useful way. Remember the key to an effective shock absorber is the combination of a spring and damper. You only have a spring here. Considering how most people except for Jan Heine are chasing stiffer frames, having an undamped spring in your acceleration parts train is not beneficial.
The hubs in radial lacing are more substantial than the hubs on tangentially spoked wheels, as they should. What are the weight (and longevity?) implications?
I don't believe J-bend hubs are sold as radial-specific, so that negates some aspects of this topic already. As @Michael points out in the comments though, some straight-pull hubs are radial-specific by nature of their design, so you must be careful about that. Hubs in radially-spoked wheels are almost certainly at a disadvantage for strength and long-life though. In a tangentially-spoked wheel, the spokes tend to pull against opposing ones in a way that almost cancels out the net tension felt by the hub flanges. Contrarily, with a radially-spoked wheel, every spoke is attempting to pull the hub flange off the hub, so to speak. Sheldon's article you link to mentions this aspect. In their product manuals, Shimano and other hub manufacturers explicitly forbid radially lacing their J-bend hubs, further supporting this argument.
I understand that whether a wheel has cup-and-cone or sealed bearings in its hub is orthogonal to whether it is laced in the old or the new style. Can you confirm this is true?
Yeah, bearing type is independent on lacing style because again, the common J-bend hub is not sold as radial-specific or tangential-specific (bar some straight-pull models as mentioned previously). I'd also like to highlight the terminology "old or new style"; I'm pretty sure both styles of lacing have been prevalent throughout history, so neither is notably newer or older.
I want to buy a wheelset and ride it for thousands of kilometers with very routine, mundane maintenance with off-the-shelf components in my (modest) home shop. Which of the two types of lacings is the better bet?
I think tangential lacing gives better service life, if not for the spokes then at least for the hub. Hence, that's the option I would recommend. The time savings of radial lacing is not worth it. For your second bonus question, I'd say radial is easier because you don't have to keep track of crossings, nor the location of the key spoke.
I speculate another factor. When replacing tangent lacing with radial lacing, we are trading one weakness (the rub at each J-bend will sooner or later wear out a spoke) with another (the activation torque needed in radial lacing moves each spoke on both ends at each torque application, eventually also wearing the joint).
I don't think so. Rubbing at the J-bend occurs for both tangential and radial lacing patterns. Either way, I think it will be the soft aluminum hub which loses the battle, not the steel spoke.
In reference to Sheldon's anecdote (well, technically John's) about a radially laced rear wheel, you write:
[A]nd yet we do have precisely that: radial lacing on front wheels with disc brakes...
Radial lacing is only ever used with rim brakes. In the context of disc-braked wheels, [radial] and [successful]: pick one.
A brake's ultimate goal is to provide a force at the point of wheel-ground intersection that is parallel to the ground and inline with your direction of movement. Disc brakes achieve this by applying a torque to the hub, which transmits it to the rim via the spokes, and then the rim applies a force to the ground. With rim brakes, the rim effectively pivots around the brake in an arc towards the rear of the bike, directly generating this braking force. The hub and spokes do not feel any torque, but rather only a linear force towards the back of the bike which slows the rider.
As a side note, when discussing such scientific matters like this in our native English, let's be precise in our use of language. Spokes are not "concurrent" to the hub, they are radial. I also think the notion of "inserting" tension into a spoke is a little absurd.