If you want full force rock drums, 4 mics isn't going to get it. Most stuff nowadays is tracked with a lot of mics. One thing that is for sure though, if you don't have decent stuff and some decent experience, having a lot of mics may actually make things harder and sound worse. One big problem is that for a 4 mic setup to sound really big, you have to have great mics, great pres, a good solid drummer with a well tuned kit, and an incredible sounding room. If you have all that, than 4 mics might be able to get you a good punchy sound. I certainly agree that for jazzy stuff, maybe some R&B etc... the minimalist approach sounds great, but if you have big guitars involved and stuff, you really will need those tom mics to help reclaim some punchiness, and probably a pair of kick mics to get that snap without some serious EQ'ing.
As far as compression goes, comps will not help get rid of bleed. In fact, they will make the bleed more aparent.
As to comping overheads..... Lots of people comp overheads. The trick is to have good compressors and know how much and when. Any old compressor is not going to work on overheads. Same goes with acoustic guitars. Personally, I comp my overheads as often as I choose to comp snare or kick. I do like comping toms a little though, and I almost always comp the drum submix.
