LOL, no.
I lived briefly in what was advertised as a “dog-friendly apartment complex” in Bloomington. First thing they did after signing the lease was hand over papers about “monthly dog rent”. I neglected to fork this over. About 2 days before I left they came to my door asking about collecting dog rent because they saw me walking a dog, I told them it’s someone else’s dog and I’ve been babysitting it.
That whole situation was probably questionable on my part but I didn’t like how it was added at the very end as a gotcha. In terms of licensing a dog with a city/ town/ whatever- absolutely not.