>> Every accident is an example of multiple things going wrong at the same time.

You are defeating your own argument :-) Its exactly because every accident is an example of multiple things going wrong at the same time...that you need...multiple layers of control and safety to catch it through each hole of the cheese.

Like...another controller?

One of the things you learn as a pilot is how to recognize that you need to go into emergency mode if you will. Call it high-alert if you want.

You need to recognize when something is out of the ordinary and treat it as an emergency (perhaps not a literal pan-pan/mayday emergency) sooner rather than later, and do things that may end up to have been unnecessary (like executing a go-around because emergency vehicles were on the move).

One controller on two frequencies is another example - that works fine in normal situations, but during an emergency response, perhaps the channels should be mixed; giving the pilots in the air a chance to hear the incorrect clearance onto their runway.

After all, an active runway is really more of an "air" control thing than a ground one.

The pilots would execute untowered approach procedures, a small airport with little to no traffic and VFR flight you may self-announce on frequency, a larger airport you go back to approach, etc.

Am I misunderstanding the implication in your comment that things would have been safer had there been no ATC at all?

Because the parties involved would be more careful if there were no ATC?