Typically on the U.K., if a service is rowdy and feels unsafe the guard will hide in their cabin and never emerge to do a ticket check.

In other words a no difference in personal safety between a driver only or driver and guard operation.

I’m not aware of any evidence of reduced safety in any category after introducing DOO, and if there as I suspect unions would be screaming from the hills. The only measurable impact I’ve seen is on accessibility (which doesnt mean that’s not a consideration)

Well, typically, they start with safer cities, something that's out of the purview if the MTA.

That totally flew over my head, sorry! Violence in the train didn't even occur to me while reading the comment, I thought they meant something on the lines of "the driver will have better visibility when opening/closing the doors on the front train so it's safer to go there so they cannot accidentally close them on me" or something similar. Now of course they meant there's less chance of violent behavior near the train driver, and the comment makes a lot more sense for me now.

Note: I do take the train daily, just I live in Tokyo

American cities are less safe, but the NYC subway is quite safe. Train operators will never leave their cabin no matter what (part of the rules of the job), and so do not enhance the safety at all.