"In terms of cleanliness, which is also an issue of public health - why doesn't MTA have a dedicated crew of 4 or 5 people with a power washer, soap and squeegees to move methodically through each station, working on the weekends or overnight? "
Can't have it, because the MTA is not in the moving-people-business, they are in the wealth-transfer-business.
In fact, MTA have been investing in vacuum cleaning systems for the tracks with the aim of reducing fires that lead to delays. You're being disingenuous. Here's an article:
So it's frankly absurd of the commenter to say that just 4-5 people could manage this task. One manager mentioned in the article leads a team of 300(!) cleaners.
They do have those teams. I've seen them work; they've got power washers, and they blast the stations. They cleaned my previous-local station once every few months, at least.
The stations don't stay clean because they move millions of people per day, not all of whom are clean. Today I saw a kid throwing up on her way into the station; she and her mother were somehow polite enough to pause above a drain to do so. Combine that with people tracking upstairs dirt in, and littering, intentional and accidental (I dropped a candy wrapper while getting my kid home; I'm not stopping to pick it up mid-tantrum), and you've got a pretty messy situation.
"In terms of cleanliness, which is also an issue of public health - why doesn't MTA have a dedicated crew of 4 or 5 people with a power washer, soap and squeegees to move methodically through each station, working on the weekends or overnight? "
Can't have it, because the MTA is not in the moving-people-business, they are in the wealth-transfer-business.