It's been done on the Honda HA-420 HondaJet.

https://en.wikipedia.org/wiki/Honda_HA-420_HondaJet

The pylons would have to be stronger (heavier) to account for column buckling loads. Servicing the engines would be harder. The under-wing engines are designed to fall away if they fail catastrophically, this would be more problematic with an over-wing engine.

Probably something to do with pitch. Imagine the center of lift(?) on the plane. If the engine is below that point, it would want to pitch up, if above, it would want want to pitch down.

Edit: Remember the whole Boeing Max problem was caused by placing the engines in a non optimal spot.

(This is pure conjecture)

Yes, the reason for the engine position on the 737 Max is that newer hi bypass ratio jet engines takes a lot of place. As the original 737 was designed for flying with much smaller diameter P&W JT8D, it stands quite low on the ground with relatively short landing gear .

Thus, with newer and newer hi bypass engines , the engine pods had to be moved further up and front of the wing, which in turn changed the flight characteristics compare to the older versions. With the Max ,enough that it would have required client airlines to have to re-train their pilots on a new 737 flying differently than the original 737 they were trained for.

And here enters the infamous MCAS which was designed to keep the original 737 flight characteristics on the 737 Max, it was selling argument for the 737 Max, airlines buying it could have a « new » plane with state of the art economic engines, without having to pay for re-training their pilots. Not a total success…

This is a big part of the answer. Usually when you're adding power, its because you want to go up so the last thing you want to happen is for the nose to go down. The higher up the engines are relative to the center of mass the more of a downward pitching moment you'll get.

Also, I believe (and I'm very much not sure about this) but the above wing mounts like the Honda Jet can have nasty implications for flutter or some other structural issues if you aren't really careful. Its like the dynamic instability of trying to hold a stick at the bottom vs the top.

Maybe the lower pressure, and particularly at close to/at stall speed, turbulent air above the wing reduces the effectiveness of the engines? So you probably need the engines mounted further from the wing (longer, heavier pylons) than an equivalent under-wing mounting?

That and center of gravity is why they stick out in front of the wing already for under-wing engines. You'll also notice the cowling slopes down and is not flat to the airflow for the same reason, to ingest air when climbing.

Some decent responses, all of which may be true, but something not mentioned is that it's simply easier to inspect & maintain engines that hang down.

Noise