Assuming a steerer/fork/brake/cable setup that does not rely on the stem facing forward: is it safe to point a stem backwards as a way to reduce seat-to-bar reach (i.e. as a way to 'fit' a too-large bike to a smaller/shorter person)? If not, why not?
No, it would not be particularly safe. The steering would get extremely twitchy and difficult to handle.
In the BMX world, they use minimum offset or zero offset necks for flatland. The minimum offset options allow you shorter reach without causing problems being backwards. These are some options (the neck/bar combo might not help, but it was shown as examples of options that exist)
In the picture you see a zero offset zero angle bar-neck combo, a minimum offset S&M neck and a Kore neck on a Morales:
The handling issues would depend on the rider's common hand positions vs the steering axis. Generally the hand positions for most stability would have the hands forward of the axis.
Steering issues aside, I would think that even if you got the reach aspect of the bike to work like this, there would be many other problems with the fit of the bike. Could you even stand safely over the top bar? Could you drop the seat low enough to reach the pedals?
Also, the headtube and stem are usually slightly angled. On a mountain bike or especially a road bike, you probably wouldn't have much movement available, as I think the handle bars would meet up with the top bar.
Assuming, as the questioner did, that we are not considering cabling and such, Whether or not to put the stem facing forward or backwards depends on the handlebar shape and placement as well as where you hold the handlebar. I think the physics of bicycle stability is pretty complicated, in any case.
There may be analogies between holding an automobile steering wheel at the "10 and 2" o'clock positions versus the "8 and 4" o'clock positions (or even one-handed at the 6 o'clock. In the car, though, we generally don't use the steering wheel to support ourselves, except during cornering. If you are making a hard turn to the right in a car, then your body will shift to the left. If you are holding the upper part of the wheel (10/2), then that body shift will help pull the steering wheel back towards the center. But if you are holding the bottom of the steering wheel (6 position), then the harder you turn, the more your body will cause the steering wheel to turn even more to the right. So, holding the upper part of the wheel would be more "stable" than the bottom, especially in an emergency.
On the bike, we do put weight on the handlebars a whole lot more, and emergencies can throw us from the bike!
Without holding onto the handlebars (or very lightly), the weight of our body and the bike serves to help keep the front wheel tending to point straight forward because of the way the fork is at an angle and the way the wheel axle is off the axis of the steering tube/headset. At the same time, there is a force of, say, road or hub friction that pushes the front wheel to twist towards the back. The angle and weight should overpower the push back.
Let's now suppose that we have a somewhat standard stem, facing forwards. Now also suppose that instead of riding without holding the bars, you ride by holding onto the end of the stem that clamps onto the handlebar, right in the middle of the bars. If you are putting your weight on the bars, as it a road bike I think, then you are probably pushing forward. This would basically make a force to make the wheel face straight forward. However, if you reversed the stem and held it in the same way, then when pushing, it would tend to swing the stem around making it turn either one way or the other.
When braking, this force of pushing on the handlebars would become even greater, even if you are riding a "cruiser" (where more of your resting weight would be on your butt).
Of course, we generally don't ride single handed (or no-handed). And so each hand can serve to balance the push of the other. If we have a backwards-facing stem, and our hands very close together, as in those stylish messenger handlebars, then braking would be very dangerous because it would be almost like riding one-handed and the bike would suddenly turn whenever you braked:
On the other hand, even with forward-facing stems, we do see hand placement that is behind the steering tube in cruiser or beach bikes or dutch bikes (as mentioned by user Kibbee), yet they are somehow safe (motorcycles also often have the grips behind the steering axis):
This (above) situation is, I can only guess, safe because the hands are so widely spaced from each other that they balance out. Additionally, maybe it's because you put less weight on your hands in bikes that use these.
With those narrow messenger bars, they are actually relatively difficult to change direction compared to mountain bikes because you don't have much leverage on the turning and because the hands serve mostly to keep you aiming straight:
Normal mountain handlebars are just wider, but that gives you a lot more leverage and control:
And the most "maneuverable" and "twitchy" bars would be something like this:
Some other handlebar setup, for reference, are below. These others also offer multiple hand placement, so the twitchiness and handling would be different depending on where you hold them. These tend to have grip locations ahead of the steer tube.
Drop and/or mustache handlebars, where it's been a bit "squished" so we see the drops:
Trekking / butterfly handlebars:
There does not seem to be a strict rule of whether hands forward, at, or rear of the steering axis makes a particular situation safe or dangerous. In general, there seems to be a mix of influences on handling (and danger from turning-when-braking) depending on such things as: