> Why does it make sense to count these people as homeless?

It's a social class thing. It's not about having a reliable, warm, dry, safe place to sleep. It's about whether a middle class university graduate's friends would have considered them to have failed at life. Living in a coffin sized apartment with cockroaches everywhere in New York is something they could see themselves doing at some point in their life for career goals or because of bad luck. A trailer is not the kind of place a university graduate lives in.

Not sure why you're getting so downvoted. You might be stating it a bit dramatically, but I've personally seen this attitude in people when living (by choice) in an RV. Many people seem to abhor the idea that someone doesn't live like them. There's broad discrimination against people living in RV parks and trailers in most municipalities.

Many cities ban you putting an RV on your own plot of land, regardless of the purpose. They often ban trailer parks, severely restrict them, etc to the detriment of many economically vulnerable people. There's often a component of racism too as some trailer parks home lots of immigrants or hispanic folks, marking them doubly undesirables.

So the definition of homeless is that it’s ‘not the kind of place a university graduate lives in’? This is absurd.

I don't think poor plumbing is exactly what we're going for here.