I'll cover some of the potential advantages by discipline, since the original question didn't state a specific discipline or disciplines. I'll address both advantages and disadvantages.
Off tarmac: MTB, gravel
In these scenarios, the advantages of tubeless seem very well accepted. You are more likely to encounter puncture and pinch flat hazards on short notice, perhaps before it's possible to react. Tubeless sealant will seal most small punctures in this scenario. Also, tubeless dramatically lowers the risk of pinch flats - note that it's still possible to pinch flat some tubeless setups, it's just that here, the tire itself is getting pinch flatted, rather than the tube.
The issues you raised are not really issues. If you damaged a tubeless tire enough to need a boot, you'd have done the same to a tubed tire. If a hole is too big for the sealant but too small for a boot, you'd use tubeless plugs for tubeless tires, whereas you'd likely have had to change the tube on a standard clincher.
The advantages of tubeless over the alternatives don't seem as clear here. I know one shop mechanic who was a tubeless enthusiast, including on the road. I have talked in person and on forums to a number of riders who say that they had tried or helped set up tubeless tires, and that they still preferred tubed clinchers. I have not personally tried road tubeless.
Jan Heine wrote in 2017 that he did not recommend tubeless pressures over 60 PSI, which he felt might cause blow-offs. If this happened during a ride, this would cause a loss of control and a crash. Heine noted that in almost all other applications, tubeless tires are run at low pressures, typically less than 45 PSI. He seems to feel that performance road tire presures may be in an unsafe zone for tubeless tires.
(Interesting side note: Zipp recently released two models of its 303 wheels, the 303S with an internal width of 23mm, and the Firecrest with a 25mm internal width. On both wheels, they state a maximum pressure of only 72.5 PSI, and their recommended pressures for most riders are very low. At my weight of 133 lbs, my recommended pressure for a 25mm tire on the 303S is 58 PSI front and 60 rear, whereas I typically run 75-80 PSI with the same width tire on a 19.6mm internal width rim depending on the surface.)
Tubeless may have been touted as having lower rolling resistance than clinchers. (NB: the tire and tube lose energy through hysteresis. Bumps in the road compress the tire/tube system. As the system rebounds, some energy is lost. No tube = less material to rebound after compression.) However, for high-performance road tires, where tubeless and standard clincher models of the same tire exist, Aerocoach documented that tubeless clinchers had similar rolling resistance to the standard clincher versions with latex tubes. (NB: latex has much lower hysteresis than butyl.) They also stated that rolling resistance on a tubeless compatible tire set up tubeless and the same tire set up with a latex tube was comparable. Bicycle Rolling Resistance also documented this with MTB tires, and they also documented this with the Schwalbe One tubeless and the One V-Guard tubed tire (comparing latex, light butyl, and normal butyl tubes). Of course, a tubeless road tire should have slightly lower rolling resistance than a comparable road tire with a butyl tube.
Josh Poertner, owner of Silca and former employee at Zipp, discusses latex tubes on a podcast here. They are a bit trickier to mount and they do require daily inflation. If you twist the inner tube while mounting, it will likely blow out, and this phenomenon may have given them a poor reputation for durability. This is user error. Poertner reports that latex tubes are actually more resistant to punctures and pinch flats than butyl tubes. I personally use latex tubes on the road.
Note that as the standards for tires and rims solidify, the tire-rim fit is likely to improve, thus improving the reliability of tubeless tires further (especially in terms of consistently fitting to rims). Their rolling resistance could decrease further with evolution in tire materials and construction, although I'm not sure how this would improve their position relative to clinchers with latex tubes.
One unanswered question is how reliably road tubeless seals after a puncture compared to lower-pressure tires. My hunch based on feedback from some users I talked to was that road tires might lose too much air before they sealed - remember that performance road cyclists use much higher pressure than gravel cyclists. I wasn't able to substantiate this, however.
Current tubeless tires are probably not optimal versus the traditional gold standard of tubular tires. However, the logistics for tubular tires are very different from tubeless tires, and most amateurs and many shops may lack the skill to glue tubulars. Either setup should be superior to tubed clinchers, based on experience in other non-tarmac disciplines.
For some time in the early 2010s, CX tubeless tires had a reputation for burping in corners, i.e. the seal broke just a bit and you lost air. This is obviously bad. In cyclocross, riders often run tires at very low pressures, e.g. <20 PSI, to increase traction while cornering. Tubular tires have been regarded as the optimal setup, provided they were glued very tightly to the rims, because they can be safely run at these pressures. They are also very hard to pinch flat, and they obviously can't burp in the same way that tubeless tires can. I haven't surveyed professional CX racers, but I suspect many of them might still regard tubulars as optimal.
Moreover, UCI-regulated CX is limited to 33mm tires by regulation. This stems from the evolution of the sport, but I believe it persists only due to tradition and regulation. Amateur riders, even if they participate in a UCI-regulated race, will not be disqualified for using wider tires than this. In any case, it may be that the optimal CX pressures and narrow tires make it hard to eliminate burping in corners.
Alternatively, as tire to rim fit continues to improve, this issue might also disappear. Even in 2016, November Bicycles reported that with their preferred rims and tires at the time, they and their riders experienced very little burping. Cyclocross Magazine reported similar in 2018, and they noted that tubeless tires were getting some uptake by professional CX racers.
In any case, amateur riders can simply show up with their existing gravel wheels and presumably tubeless tires. I don't perceive that the advantage of tubulars is enough to justify getting a separate set of wheels and either learning to do a proper glue job or paying someone to do it. (NB: if you don't glue well enough, you can roll a tubular tire off the rim when cornering. If you crash and you take someone down because of your sloppy glue job, you need to apologize to everyone profusely and pay a professional.) Another very minor point is that on the road, tubulars seem to have higher rolling resistance than the best clinchers. In part, this might be attributable to the layer of glue. If true, this would also apply to CX tubulars.
Touring and commuting on road
Riders here benefit from wide tires. Wide tires mean lower pressure than performance road settings. As stated above,I expect tubeless tires' benefits relative to standard clinchers to improve with wider tire width and lower pressure. So, perhaps there's another possible use case here, especially since the sealant should defeat many small punctures. Last, I'd expect many of these riders to strongly not prefer latex tubes, so tubeless tires should be the lower rolling resistance option also. (NB: you could split the difference with light butyl tubes.)
I am not familiar with tires used in this space, so I can't really flesh this section out. It's my sense that like many things in cycling, tubeless tires originate from the high-performance side of the sport, so manufacturers may simply not have thought to develop good touring and commuting tubeless tires. Here, I'd expect the net benefits to tubeless to exceed the performance road scenario. The question is, does that justify a switch to tubeless? Some commenters on other answers said that they had benefitted from the sealant, so your riding conditions may be the main determinant here.