For the low speed scenario, Boeing invented the "airspeed low" GPWS call out. If that doesn't wake you up and cause you to advance thrust, you shouldn't be sitting in that seat either.
Introduced after THY stall at AMS. So once again the solution/back-up is to insert another auto-function between pilot & a/c. As we seen over the years this only encourages, subtly, the pilot to reduce scan and rely on automatic warnings. Shades of SFX B777 and others. I suggest, strongly, that if THY had been a manual approach with manual thrust, and followed the exact same manoeuvre, they would not have stalled. Add to that the use of ARM, perhaps better. I've never been allowed to use it on B737 so can not comment on its function in reality. (Indeed, has anyone had it kick in the save their backside? or is it just a theory?)
No, it's not a bad idea to take out the AT with a TCAS RA. If you get a descend RA with the AT in N1, you will very fast go into an overspeed situation. The AT will remain at N1 in this situation with no speed control.
OK, true, if you are in a climb; but is it that critical? However, and I've seen it in the sim many times, they get a 'CLB CLB RA"; disconnect everything, apply 3g pull and forget to add power. Now do that at FL350 and see what the speed does. Is a low speed more/less critical than overspeed? One has a clacker the other a shaker & clacker. I've also seen the "DESC NOW RA + Increase ROD". Then "Clear of Conflict" = climb back to last cleared FL and forget to add thrust. Consequence? see above. IMHO on there balance of risks I'd rather keep AT engaged. Dogmatic philosophy has its weaknesses.
Regarding SAFETY and commonality of actions: agree. I know of some airlines that encourage maximum use of Automatics, at all times: yet they perform a single channel ILS or NPA with full automatics; make a G/A = AP disconnects, but AT remains engaged, but they fly the whole GA and flap retraction in manual with AT in engaged?????