Uneven acceleration, effects on an engine?

Factual Questions
1

I know some people who, instead of simply keeping their foot on the pedal properly at a constant RPM to maintain speed, will accelerate sharply, coast, coast, coast, accelerate sharply, coast, etc. So their foot is constantly going up and down on the accelerator - RPMs are going way up and then way down.

What damage, long term, will this cause on an engine?

And… would this affect gas milage very adversely?

2

This type of driving costs heavily in terms of fuel consumption, it also has to put more strain on the clutch, the thrust bearing and the drivetrain.

It might even have some effect upon the oilflow to some parts of the engine, most likely the top end.

It will produce more heat which will have to be dealt with too, so the fan may need to cut in more often if its one of those temperature controlled ones.