A ban on abortions, in this example, would be codifying the government's legal authority to make such a decision.
That's first order building, there is no need for rebuilding in that scenario.
With regards to the broader DOGE topic, they aren't banning anything yet that I've seen outside of the authority that we already granted the executive branch. I don't necessarily agree with what they're doing, but from the bits and pieces I can pull out of largely political reporting it does seem like they're staying within the bounds of what the executive branch is technically allowed to do.
There will be a legal debate whether there are within the rules to not spend money budgeted by congress. That will come down to an opinion whether the argument that departments are not acting in good faith or reasonably executing their mandate is found by the courts to be reasonable.
The voters I know who vote primarily on this issue want a law on the books banning abortions, they don't want to just defund programs.
By no means does that mean I can extend that view to other voters, but I have yet to hear anyone who feels strongly pro-life argue only for defunding.