A few bits and bobs I've noticed, we use a belt drive on the 20HP diesel - but a diesel is a whole different kettle of fish to a small petrol engine. Most engines won't last long enough for the heat transfer to be an issue, I've never repaired a pump on and engine driven unit effected by heat transfer - electrics do it all the time web the motors burn out but having asked at dual neither have they and they started doing this in 1975!
With a gearbox you have the following
Almost zero maintenance
Periodic oil change (Should be checked every use but easy to see through sight glass)
Keyway snatch (Slide pump off on yearly basis and re-grease) which eradicates the problem - all engine manuals will have a bit somewhere about renewing the key steel as part of the yearly service - no one does.
With the belt system
There is no actual connection to the engine which is a good thing! It reduces vibration transfer certainly - but with such a small petrol engine there is quite honestly no point, unless the engine is so poorly balanced it becomes necessary, on a big diesel fair enough but even so the plat the pump sits on should be vibration mounted not just bolted down.
When you come off of the trigger with a gearbox the gears take up the snatch effect - with a belt system you are just stretching at the belt and pullys - there is not much of a real difference in wear and I would guess that the belt wears out first.
The pully will rust onto the shaft if not kept greased up (less of a problem with gearboxes)
Belt will stretch with use and NEED adjusting as it will start to slip especially in damp conditions unless the correct tension is kept on the belt. Most customers won't do this - many don't check the oil let alone tension a belt drive.
Belts have a tendency to react with chemicals.....
If I didn't think the hassle would out weigh the fairly chunky saving we'd use them