I don't think I've heard even the strictest pro-prison people try to seriously make the argument that prison is cheaper than housing for the same time periods of detention. Prison is really expensive, it's in a lot of ways a strict superset of housing. Even just holding people in preparation of a trial and getting them convicted is really expensive. Where are you getting these numbers from?
> No, we are arguing about where that responsibility should be taken
I mean, if you want to argue about that, sure. But my argument is that they're on the street right now and saying that they should have avoided getting addicted to drugs in the past is not particularly useful to the current conversation unless you have a time machine handy.
> no criminalization = no judge to force rehab, of course
Look, this is just a different argument. Are you arguing that rehab does actually work, but we need criminalization so we can force it? I have seen people argue that point, but it's not really an argument about personal responsibility, it's an argument that the state should have even more involvement in rehabilitation than it currently does.
Of course, it isn't free. It is cheaper than what we are currently accomplishing through the homeless industrial complex ($10k/month just for a place to park a derelict RV at a recent project), so let's not kid ourselves that prison is more expensive than the alternatives: it isn't. Someone inside also can get treatments and will find it much harder to acquire drugs (fentanyl is much more expensive in prison and very cheap outside of prison).
> But you're arguing we don't have means to do that.
No, we are arguing about where that responsibility should be taken: when they want to go to rehab (which they may never want), or before they actually start doing drugs.
> People are already on the street addicted to fentanyl, you can either leave them there or the state can try to expend money/resources getting them off of the street and dealing with that addiction.
We have fewer options than that. Usually its a combination of both: the state (actually the city) expends money to deal with the addiction, but they are back on the street in a couple of weeks because they want more drugs and we can't actually force them to let us deal with their addiction (no criminalization = no judge to force rehab, of course).
> If you think prison is effective rehab and that it's worth the increased cost
Prison is cheaper than what we are spending on the problem right now. We've passed that point a few years ago.