More microphones generally give you more options but that's not to say that those options are any better or worse.
I treat close mics as luxury items. If I can't get the sound I want using overheads after tweaking, I'll add a bass drum mic or a snare mic. If I'm still not getting it, I might add one or two more for the options. Certain styles of music call for more processing - which in turn usually means having more options (and more mics). That's usually the case in Rock/Metal/Pop production but if you extend your listening outside of that, where the drum sound is more natural and based on room capture, you can create sounds that are just as satisfying with almost no equipment and a lot of knowledge.
When I was recording more seriously, I learned quickly that if you didn't have a good overhead sound, then your recording is usually terrible - no matter how many mics you shove in front of your drums. I've always used a minimalist approach compared to my peers but generally get a sound that is more satisfying (to my ears) and one that takes half the time to set up and a quarter of the time to edit.
It's like composing poetry. You can write beautiful poetry with thousands of words ('Rime of the Ancient Mariner', 'Beowulf', etc.) or you can write poetry with very few words (good Haiku). Or you can cook with a huge myriad of complex ingredients and get a great result, or cook with very few and get a great result.
It's about options. With recording, the overriding, basic premise is to get that overhead sound right. Without that, unless you're doing something special (like going for super-separation alá Joy Division's first album) then your kit sound will be lacking.
EDIT: Try to tell me this isn't a brilliant drum recording in context of the music. Despite it probably being only one or two microphones (and the tape decay evident early on). It's fantastic
. All about placement and the right room.