A better idea might be to provide the homeless with a better standard of living, therefore making them nicer to be around on public transport

Some of them aren’t merely lacking access to resources. Mental illness is part of the picture too. Trains and busses are warm comfortable places for such, as well as the criminal element. People think of bus and subway stations as dirty and often dangerous places, not just in the USA.

You can't make them wipe.

I don't know if they're un-homed or not, but I've encountered a lot of people smoking, shouting, or making a mess with food in rail cars, making them unusable for everyone else.