It's a personal choice, and one based on what kind of sound you are looking for, not to mention the types of mics you have and the space you have to record in. All those things will affect the outcome of whatever method you use.
Having said that, there is no reason you can't get a great drum sound with two channels.
Close mic'ing sources does not lead to a natural sound. You will have to EQ the crap out of things, and that alone makes it harder than placing one or two good mics. Add to that phase problems, and possibly messing around with gates and you often make the job harder with multiple mics, and often not as good (unless you know what you are doing or the sound you want simply requires close mic'ing).
Omni mics can be used to get a stereo image of the kit - and omnis often have enough low end to get to get the bass drum without a separate mic. Also, one omni mic placed in the middle of the kit a few inches above the bass drum, near the drummer's right knee, kind of between the snare and the rack toms (low enough so it does not get whacked) can sometimes make the whole kit sound close-mic'd (though that would be in mono).
If it were me, I'd mess around with a stereo pair before messing with trying to mix everything live to two-track. At the very least, maybe get the stereo pair as close as possible and then just mix in a little snare and a little bass drum.
Trying to mix anything more than that without being able to go back and adjust anything is asking for trouble, IMO.
