Well my point is two-fold. First, what you say here is my point, all branches need an _enforcement_ arm. Today Congress has the Sergeant at Arms and courts have bailiffs and may deputize members of the Executive Branch.
However that's clearly inadequate in the face of the Executive's current balance of power. A rebalancing is necessary imo.
Could that result in a Roman-esque problem of the three branches having "tug of wars" with each other's law enforcement arm, but I don't think so. We have this problem today with the dozens of law enforcement organizations within the Executive...which brings me to my second point!
My second point is that carrying out the law in the Executive was clearly the wrong choice. The Legislative branch should actually carry out the law, i.e. USPS should live under a committee in Congress, and mail fraud would continue to be prosecuted by the Executive.
I'll caveat that I'm had waiving a lot here, but I hope we can all agree at least on the problem statement; too much power has concentrated in the Executive and _drastic_ measures would be required to resolve that situation.
The founders were right that nobody can be trusted to neutrally enforce “the law.” If you could trust Harvard graduates as a class to do that, there would be no reason for checks and balances or separation of powers.