There shouldn’t have to be a list in the first place. If we can’t trust them to be on a plane they should never have been allowed in in the first place. If they are criminals, they should be charged. If they’re guilty, convict them.
This is about a “terrorist watch list” not even the smaller “no fly list.”
I would posit that it makes more sense to have such purchases quietly trigger a closer watch, than to stop them.