I think overheads are the most important mics. One of the first Hollywood engineers I ever met told me he wouldn't record a drumkit without condensers for overheads. They are for the stereo image of the kit and it really wouldn't sound right without them.
Close mics are definately a big part of the modern sound, and have been since the 70's. The room has a huge effect on the sound today. In the 70's, studio rooms were very dead spaces. It's why 70's drums sounded like, well, 70's drums.
Overheads pick up the articulation and punch of the kit. Close mics fill in the body. Granted, you can do alot by close micing and letting the bleed pick up the cymbals. I've done both and much prefer to have a set for the overheads. Over time I've been lucky enough to build up my gear to be able to track every drum and mic. I've had some good recordings that were done with minimal equipment and a great deal of jury rigging and creativity.
There really are no rules, but there are excepted and established practices.