Chesterton's meta-fence: "in our current system (democratic market economies with large governments) the common practice of taking down Chesterton fences is a process which seems well established and has a decent track record, and should not be unduly interfered with (unless you fully understand it)".
For the Chesterton's Fence objection to properly have applied to the NHS, it would have had to have been the case that no one could explain the historical lack of NHS. Yet I think it's pretty easily explained by governments' values over time: first kleptocratic, then libertarianish, and only becoming utilitarian roughly around the time of the NHS, to simplify heavily.
The more advance versions of the fence apply even if the reasons for the fence are unknown or bad (or badly explained).