It's less expensive in aggregate, but on an individual level rates will almost certainly go up (even if they're lumped into taxes). Individuals cast votes, so if individuals are negatively impacted, they're going to vote against it.

The only way to dodge that is to subsidize it, whether by reducing the budget elsewhere (cough cough the F-35 program cough cough) or raising taxes (cough cough on the ultra-rich cough cough).