Can someone explain why a mic with both battery and phantom power costs less than the same mic with phantom power only? Why would you not want both?

Phantom power is usually supplied at a reasonably high voltage - more than in required to run the preamplifier in the microphone. If only phantom power is present then circuitry is required to derive the lower voltage for the pre-amp. If a battery is also present then the high phantom voltage can be used to bias the capsule while the lower battery voltage can be used to operate the preamp. It's a pretty shaky hypothesis but about the best I can come up with.

Can someone explain why a mic with both battery and phantom power costs less than the same mic with phantom power only? Why would you not want both?

There can be several explanations depending on the mic. Condenser mics that have an internal battery invariably are based on permanently charged "electret" mic capsules which are often (though certainly not always - there are many very fine electret based mics out there) considered inferior to "classic" condensor mics that require full phantom power. Also the dual power battery/phantom mics are somewhat larger and heavier than the same mic in the phantom only version in order to make room for the battery. For example, the Rode NTG-2 is 2.5 inches longer than the NTG-1 and a couple ounces heavier yet they are the exact same mic except for the powering.

Condenser mics that have an internal battery invariably are based on permanently charged "electret" mic capsules


"invariably"? NT4. NT3.

"invariably"? NT4. NT3.

I stand corrected - let me rephrase to "internal battery-powered mics usually are based on a permanently charged electret capsule ..."