She was a relatively slow BB. so that she carries three aircraft is probably for her to have three times as likely to spot the enemy. so she can put an intercept course much earlier, or vice versa.
I'd also wager to ensure that there's at least one aircraft up at all times (one airborne, one on cat ready to relieve, one getting fixed up, fueled, or having its crew rest). New Mexico wasn't necessarily slower than the rest of the battle fleet - in fact, at 21 knots, she was right in line with every other battleship in commission then save for the North Carolinas and whatever SoDaks were just coming on line (and they weren't
that much faster too, not like the Iowas).
Do also note that the fast battleships had two catapults too, just both occupying starboard and port on the fantail. I believe with the older battleships there was only enough room for a cat on starboard so the second one had to be shipped on a turret.