Problem with air flow and a/c

The actuators go bad over time. They are simple devices and can be easy to replace. The "can" being entirely dependent on how they are mounted in each model car, not on the design of the actuator itself. They are not easy to get to in a Prius. See for instance this video:

There are 3 HVAC actuators in cars, these are:

1. Blend door (mix hot/cold air)
2. Mode door (where the air goes)
3. Recirc/fresh door (mix fresh and recirculated air)

The problem in you car appears to be the mode door, in Toyota speak the "air outlet control servo motor". It does not look at all easy to get to, as it is just under the top of the dash, on the driver side of the evaporator. We had a problem with this very part after they replaced our evaporator - they forgot to plug the actuator back in. Luckily the shop that did that repair acknowledged their goof up and fixed it.Otherwise it would probably have been many hours of labor. Just to plug it in.

There is a slight chance that your broken clock spring (the part of the steering wheel that lets the button presses reach the rest of the car) is causing this. If the wire is shorting on something it might be sometimes confusing the MFD control. If that was the case there is a chance that the MFD control might not work, then turn the steering wheel to another position, and then it would work. The clock spring is a lot easier to get to.

 

The gen 1 and gen 2 ones can also be easy to repair (simple cleaning, cost of some electronic contact cleaner if you haven't already got some), provided they have not been dithering so long as to wear through the tracks.

That's covered in this thread: No, that wasn't a mouse in the heater.

The outlet select actuator isn't the easiest of the three to get to, but it isn't the hardest either. It's on the driver's side, a bit higher up than the air mix actuator (which is the easiest). It's a bit harder in gen 2 than gen 1 because the brake ECU is a big ol' thing in the way. But I think that thread has some stories where it's been done.