Pressure cookers -- why are they good at things normally cooked at low heat?

Braises are, by their very natures, cooked to well done. They achieve an internal temperature well above 165 F which will make every meat well done.

Please see:

Why would a pressure cooker shorten a braise time?

for a detailed discussion on how the collagen to gelatin conversion takes place over time, and is made faster in pressure cookers.

The fact that the cuts that are suitable for braising are exactly the ones that allow the slow conversion of collagen to gelatin is what makes the pressure cooker suitable.

The real issue with cooking braises low and slow in the conventional oven is that at sea level, the internal temperature cannot get very high, so you need time for the gelatin to collagen conversion to take place. There isn't much point in raising the oven temperature higher than required to allow the time for this conversion, and it prevents overcooking or drying out the outside of the food while the conversion takes place. The meat will still be quite well done; it is only moist and succulent because of the melted fat, and the gelatin lubricating the meat fibers providing that slow cooked unctuousness.

In a pressure cooker, the ceiling temperature is raised, so the time can be shortened. The inside of the food is still quite well done. No loss to quality (since the food would be well done anyway), but a much shorter time.

If the food was not suitable to be cooked well done, the pressure cooker would be far from ideal, as it would certainly overcook the inside of the meat.

Note also that you have listed two special cases where foods are cooked at lower temperatures to avoid agitation (from the bubbling and boiling of the water), rather than because of issues directly related to time and temperature:

• Stock. Stock is cooked at a simmer to avoid the turbulence and circulation from the bubbling and boiling leading to more dissolved, emulsified or suspended particles in the final product. That is, the goal is to keep the stock clear instead of cloudy. If you are not concerned with this aspect, it can be cooked at a full boil.

• Beans are cooked slowly for several reasons, of which the main one is convenience. Cooking them at a full boil would require more attention (so they don't burn on the bottom), and is not terribly feasible in an oven, which is the easiest way to do them. Also, by cooking below the boil, there is less agitation in the pot, and so less splitting and sloughing of the bean skins, which some people find less than pleasing.

In the pressure cooker, you will not get this kind of agitation, because once the pressure is achieved and the food is at equilibrium, it is not going to be going at a full boil, but more of a simmer, but a much higher temperature simmer than is possible at sea level pressure.