I think perhaps your biases are showing in the language you deploy (junkeis, free to destroy). You're asking for evidence that's readily available, if you want it, from studies to meta studies. The evidence ranges from conclusive to inconclusive, which isn't surprising given the many different types of implementation and existence of support ystems (or lack thereof).

In terms of cost, we need to look at the total social cost. If (big if) we were to assume that property destruction in housing units costs money, it is no strech to think that any marginal decrease in for example medical expenses (much more expensive in total social resource terms) more than make up for it. And a marginal improvement in a long-term expensive social problem would easily justify a high initial upfront cost.

I'm not saying you're wrong for asking the question, just that I have no problem accepting the findings that housing first is a cheaper solution in the long run if it gets more people clean and off the streets--as the evidence indicates.