https://www.un.org/en/about-us/universal-declaration-of-huma...
There are reasons, although one might disagree with them.
Article 13 concerns freedom of movement within one's own country, and the right of return thereto.
Many articles in that document provide hints/the spirit of reasons one _might_ consider immigration a human right. I think it is easy to entertain the idea and think of potential reasons for it.
A different matter is if that is indeed the case (your point). Still, I believe there are good reasons for it: the human rights declaration points at many of them, in many different articles.
For example, here is one reason (even for self-interested people, Milton Friedman-style): equality of opportunity might give an opportunity to somebody who is more capable (who knows who is the next Einstein). It will? not necessarily. But it might? definitely, it might. That is one reason.
I a not naive in regards to implementation. But there are reasons (like the above) for considering it.
No, because the NIMBYs don't want that, and if the local government has power over whether dense housing is built or not, the NIMBYs will be sure to get their local legislators to prevent it.
Sometimes it actually is immigration that is causing problems.