I am in favor of helping people who need help. If giving someone $400 of federal funds means that $1000 gets sent to a homeless shelter, than I am in favor. Because that $1000 will likely do more good than whatever that $400 was going towards.
If billions get sent to help homeless people, but some rich jerk also makes money by running a scam, then I am still in favor. Because helping people is more important to me than seeing jerks suffer.
I think tax breaks are an incentive, and people do more of what they are incentivized to do.
But if you disagree, then there is no reason to limit ourselves to charity. We have tax rebates for education, day care, energy efficiency, etc. If we eliminate the charity deduction on the theory that the money would have been spent anyway, then we should also eliminate deductions for college savings, day care, solar panels etc.
We end up with a government that doesn’t care where you spend your money, which I think is a step backwards for progressives.