I'm reasonably sure it would be possible to implement appropriate DSP Voodoo Magic (aka finite response filters) on the Teensy that does a _pretty_ good job of all of these things.
However, I agree with the OP that it does have a fairly large number of shortcomings:
-- The number of man-years that have been spent on commercial products is huge, and they provide a highly optimised solution in a competitive domain. My late grandfather had, in the 1970s, a hearing aid with feedback reduction powered by an analogue computer (aka "electronics") that hung around his neck.
-- A lot of the tuning parameters of these algorithms really are hardware specific and would require quite a lot of tuning /iteration
-- At the end of the day, a Teensy is a moderately large rectangular board that will not fit behind your ear, has nonzero power requirements, and is a general purpose CPU. A 3D printed case is an expensive way of making a plastic box to put it in. If you were going to go down the open hardware route, you'd start somewhere very different, with power efficient dedicated DSP units on a small, thick multilayer board milled to be a bit more ergonomic. A modern hearing aid needs a new battery every month or so, and is powered by a 0,54 g 1.4 V 180 mAh battery (that is a 4x6 mm cylinder [h x d]). You're not going to get anything like that for a general purpose CPU.
Still, this is a fun project, and I commend people doing it. As ever with anything to do with the USA and healthcare products, however, I can't help but think that their efforts would be better spent trying to get universal healthcare. The cost to the NHS for two hearing aids, multiple fitting appointments included, is around £400.
I'm no expert in the field, but it's my understanding that those features are why modern devices allow people to hear in noisy environments. Feedback reduction especially, which is not easy to deal with (tl;dr, the mic/speaker are mechanically coupled, with a poor seal and loud enough environment you get feedback and the DSP has to compensate).
And in terms of battery life, I don't know. I do know that most battery powered audio devices with DSP throw floating point math out the window from the get-go, and I haven't seen a job opening for DSP in hearing aids that didn't mention fixed point math in awhile. I don't know of any processors that fit the bill there however, those things usually have a proprietary IDE/debugger/flasher you need to pay for.
