That's pretty much exactly why.
In virtually every test that every country has done, it ends up costing less money to just... Give people money.. Than it does to fully fund a support system for the poor. I really don't have any desire to dig deep into it, as this isn't the thread for it, but there's plenty of research if you want to look it up. The long and short of it is, if they give people enough money for things like rent/mortgage, they end up not needing the services for welfare (or relying less on it). That administrative overhead relieved is a larger amount relieved than what they're effectively handing out.