My impression of the Housing First movement is that they believe that housing more people is in itself a good thing and people without housing is a bad thing.

I would probably agree to some degree.

So you could say of course homelessness decreases if you give homes, but that's like saying of course feeding hungry people decreases if you give them food.

The question of effectiveness, at least from the housing first perspective, here is whether or not this can be done in a practical manner and whether this has bad side effects.

This does make it a little harder to rely on data from housing first advocates if you do not share their assumption.

That being said my impression is there is some data that suggests better outcomes in terms of decreased drug usage and better employment, although I think there are some people who dispute this.

So I think there's a settled consensus that giving people houses can be done in a practical way, the extent of the benefits outside of housing is less settled, although on-average positive.

I'm not an expert though.