The point is that there are shelter beds available: many are empty. The fact that if every single homeless person decided to take a bed there wouldn't be enough

The point is that there are shelter beds available: many are empty. The fact that if every single homeless person decided to take a bed there wouldn't be enough is irrelevant, because they don't want to. If N is the number of beds needed to house absolutely every homeless person, going from N-1 to N wouldn't result in a single additional homeless person in a bed, because right now there are empty beds available that aren't being taken. There are reasons a homeless person might not want to take a bed right now, some of them even sympathetic reasons (safety being foremost), but getting up to N beds would do nothing to make them want to take one of those beds. And as soon as we did get to N beds, homelessness advocates would immediately start stipulating additional demands before anything could be done: it can't be just a bed, it needs a storage unit; it needs to allow pets; it can't be just a bed but be an entirely separate unit having a locking door for safety; etc. The "we must get to N beds before we do anything!" is a talking point that distracts from the core issue. For the record, I'd be against enforcing the laws if it were the case that every homeless shelter was at full capacity.