I would assume that someone has crunched the numbers, and come up with an appropriate means of filling the gap (likely more taxes on either property or the wealthy...which helps the poor whom are more likely to use the buses in the first place).

There's no reason to assume that. Mamdani hasn't said anything at all about providing any additional funding to backfill the loss of revenue - and a billion dollars is a lot of money, even relative to the very large budgets that NYC transit has already (it's the biggest in the country).

Plus, the same analysis holds. If you have a billion dollars a year that could be put into transit, put the billion dollars into transit. Make the public investment. Improve head times, reliability, service coverage, and safety and security on the system. Get more people to use the system by making the system more valuable and useful for the riders.

If there are people in your community who are genuinely too poor to afford bus fare, then give those people free access - don't give everyone free access. That's what Kansas City ended up having to do when they had to backtrack off of fare-free buses, as their efforts at free buses collapsed in the toxic mix of fiscal problems and looming service cuts that happens when you slash the transit agency's funding:

kcur.org - Kansas city will reinstate bus fares and reduce frequency of most routes under funding plan

Fare-free bus service is a bad idea - not because it's bad for Tesla or private cars, but because it's bad for public transit. Again, PhoolishPhilip had it right - if you value transit, you want to encourage public investment in transit, especially by the people for whom transit is most valuable, the people who ride it.