I am working on a commercial rating now 243 hours and an aerospace space engineering degree. I feel the failure is in the PTS, and the design of the stalling regime.
Stalls going into spins are not well understood by today's ATP commercial or CFI, and the regulation in the PTS standards are to blame. They call for a recovery with minimal altitude loss and its that second part is the problem. When training in trainers for ratings the full power stall procedure is to cut the power, nose up to bleed speed, then full power nose up into the stall. ALL effort is focused on stopping the stall before it develops, not allowing the stall to occur, then recovering, but recovering only from an incipient stall. Much would be gained by requiring a full stall demonstration allowing the stall to develop and not worrying about busting the alt on the recovery, many testing failures have resulted from accelerated stalls on the recovery trying not to drop alt in the stall. This may come from a misread altitude loss requirement, but the way it is enforced is a nearly a failure to allow the stall happen. The ultimate lesson that needs to be learned is that you MUST FIRST break the stall, then initiate recovery. I would care if every applicant lost 300 feet so long as they knew that they had to get the AOA under critical first. I think it is very likely that the Colgan Air Capt. never saw more than 4 intentional stalls in his life. Today pilots are taught that stalls are impossible to recover from (Cirrus pull the chute), and are taught cookbook style stalls that will likely never happen in real life.
This started with the FAA getting away from spin training years ago and has moved to the point where while training even a stall is to be avoided at all costs because they turn into spins which are now only taught once during CFI training and not even done on that check ride. Combine this with an overreliance on automation (see 777 SFO, Colgan Buffalo, UPS Birmingham) and its a very real issue of basic piloting skills being totally lost. Extremely low time CFi who don't know much of anything and its a case of the blind leading the blind. I'll be a CFI before long and I won't ever have been in ice before making it to a transport aircraft. I would much rather have gone to a cargo carrier and flown nights in the right seat than get my 1250 hours instructing, and it would have been far safer, than the current Rube Goldberg style regulations.
I would much rather have the FAA allow very low time 500 hour CPL pilots in cargo aircraft than the current 1500 ATP requirements that wouldn't have stopped the buffalo crash.

You make some valid points and as a one time FAA designated pilot examiner for Private, Commercial and Instrument ratings and Multi-engine rating, we were required to strictly stick to the current FAA flight standards. As far as stall requirements, the recognize of an impending stall was the most important thing, but like you, I think that falls short of finding out if the applicator was truly, "the master of that aircraft". After the usual check maneuvers, I always had the applicant demonstrate a 45 and 60 degree banked turn, VFR, with a plus or minus 100 foot altitude loss or gain. (I wonder how many pilots in AH could do that in the game). Most could not do it in a satisfactorily manner, so usually retraining was required before I would pass the applicant's check ride. Very few flight instructors had completed the demonstrated spin recovery technique which I think was very important pilot training. Slow flight was another pet peeve of mine, as most couldn't maintain altitude and airspeed at the same time.
The pilot of the Buffalo crash had failed instrument flight tests 2 or 3 times in his career, but he was allowed to cont flying as PIC of transport aircraft. While that aircraft model had a history
of zonal icing problems, I think the pilots incompetence in IFR conditions had more to do with that accident than anything. The fact that the crew was engaged in idle "chit chat" was also a factor in this accident.
At any rate, if a PIC doesn't stay "ahead" of his aircraft at all times, its just a matter of time before he is involved in an accident! Instrument flight on partial panel is another thing I always insisted on. If a pilot cannot fly on "needle, ball, airspeed and altimeter, then he or she shouldn't flying on instruments. All the new bells and whistles are well and good for safe flight, but what happens when you have complete electrical failure? Fortunately most good airlines insist on "raw" date instruments in the event of Elect failure, but then comes the question, can the PIC fly on raw data alone.
As a chief flight instructor for largest flight school in Atlanta, I flew with every potential new instructor and only hired about 5 out 10 because of the lack of understanding and training for the things which I have mentioned in this reply.
On your Ice comment, just remember, if it is freezing rain, climb, because there is warm air above you. If you have clear or rime ice, use your deice boots, if you have them on that aircraft, manually, not on automatic.