I personally prescribe to the “go when you're ready” method when it comes to rest periods. It's been working well for me and I also find it has helped me at meets as I rarely have more than 2 minutes between attempts and I can also warm-up fairly fast.

I don't know how you guys squat heavy on 2 minutes rest.  When I'm going heavy, I never take less than 5 minutes between squats, usually 6-7.  After each set my breathing doesn't go back to normal for a full minute, and my body doesn't feel ready to do a set until at least 5 minutes.  I used to stick strictly to 5 minutes rest and this led to failed sets.  Short rest should be left to hypertrophic exercises when you just want to kill your muscles to give stimulus for hypertrophy(e.g., supersets, assistance movements).  If you're looking for strength gains, give yourself more rest on compound movements.

I think this all depends on how "heavy" you're actually lifting during training. For me, using 5/3/1 means that I'm sub-maximal pretty much all the time except for when I'm doing my meet prep. So, in a program like this I can get away with shorter rest periods. However, if someone is training with a higher percent of their 1RM then of course more rest would be necessary. Great advice in general though.