The driveshaft popping out of the wheel axle is pretty much common on the TA05 type cars as well. You have found the solution however. Later, universals.
About the steering becoming misaligned I would check to make sure there is no binding or any other problem with the linkages, suspension, etc. Assuming everything checks out, I would guess it is a servo saver issue. The kit savers on these kits (and even the high torque upgrade saver from Tamiya) are pretty crappy. What happens is that for every shock in the steering, the circular springs hit the plastic shoulders on the saver arms and chip away a bit of plastic so the spring doesn't rest against the shoulders where they did when new any more. This allows for a new "zero" position to be set and of course your wheels are not going to be straight with this new zero position.
Get some decent saver such as one from Kimborough and you'll be fine. Plastic everywhere doesn't help as you realised, but the saver really leaves a lot to be desired.
The other way around it is to get a serious servo and go without a saver, but I am not a fan of this idea. I run some of the best servos there are in my cars and still use savers. After all, a JR servo (8715 I think is the number for the US market) is almost the price of the whole damn car!