I think Trump might actually have a legal argument for his action. If building the wall is seen as enforcing existing immigration law, executing the law is his actual job.
Not that I agree with his action in any way whatsoever, but if it stands on this principle I don't agree that it essentially expands Presidential power nearly to infinity. If a Democrat President were to try the same approach for, say, healthcare reform, they would only be able to do things within the scope of current law. That's far short of socialized healthcare.