Living in a hotel does qualify as homeless in my opinion. Same as trailer or anything that is not a fixed home. The definition of homeless doesn not equate to just to simply sleeping under the stars.
Why does it make sense to count these people as homeless?
And even if you're renting... Why count someone who rents a trailer as homeless but not someone who rents an apartment?
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.
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.
Your public contempt is reciprocated by the people you do not respect.