The most pragmatic objection to this would be that everything you do prevents the construction of housing - if you build a city hall, you are preventing an apartment block from being built on the same land. Taxes prevent the construction of housing because the reduce the funds available to home builders and buyers. Property rights prevent the construction of housing because they would prevent me from setting up a tent in your front lawn. Making housing a right is a wellspring of endless absurdities, unless you are willing to treat it as a "maybe" goal. Maybe-goals and human rights are disjoint sets.

>Of course, like all other rights, it would be balanced against reasonable government interests...

So, let's look at a real human rights example, being assassinated by your government because you are protesting something. The dictator might claim that they were balancing your life against reasonable government interests - the reasonable response would be, "no interest is so reasonable that what you did would be justified." That's the thesis of human rights, if anything is justifiable then you don't believe in human rights. It's not that complicated.

So, if you think that housing as a basic human right can be suspended for reasonable reasons, you either don't really think it's a human right, don't believe in human rights at all, or are proposing a distorted crazyland.