Metro's take on this problem is to add more police to the equation, but that's a sisyphean task. As long as there is no way to ban people from the system for bad behavior, having a few random cops walking around isn't going to change things. There's also a problem of people who behave badly but not in a bannable way, e.g. behaving creepily toward women but not fully crossing a line.

My wife tried using the bus system for her first six months working in downtown LA, but ultimately gave up because she was getting harassed regularly. I stopped using the metro after a rider on my train walked up and down the train threatening to stab everyone and nothing was done about it.

You would need a uniformed officer on every single bus and train in the city to begin to chip away at this problem. I suppose it's a budget issue in a way, but it's more of a culture issue.

I’ve seen people peeing on the track multiple times on the blue line and human feces on the red line. Why would I want to keep using that service?

>so safety and cleaniness have nothing to do with the budget?

No, they do not.

The safety and cleanliness of public infrastructure ultimately stem from the culture of the people living there.