The trouble is the tyres arent that dynamic. They have a fairly consistent wear rate, so you dont get 30 seconds of advantage from 20 fast laps, so the result is everyone 'saves their tyres'.
I agree, your solution would be the best, but it would require a complete redevelopment of the tyres, and then a redevelopment of all the cars to run on those tyres, and with in season testing banned that will never happen.
Forcing pitstops is a short term stop gap that would stop the 'save the tyres' mentality. Your 'stop 2 or 3 times' idea would mean a top team would need to be able to pull out 90 seconds over their rivals just by pushing a bit harder. Thats 2 seconds a lap... it simply wont happen with the current setup.