I don’t think any harm is done at all with any machine in breaking it in gently. With a brand new out of the box rifle, you have to mount a scope and zero it.
What harm does shooting it slowly and cleaning between shots do?
When putting on a new scope / mounts you will shoot half a dozen rounds. You might get lucky with two or three, but you need to check that it groups with your chosen ammo.
It also pays to fully load the magazine and check that it does not fall out or open under recoil.
You are not waisting in do all of the above. Especially if you clean between rounds and let it all work in.
Just the same with a car, truck or any other engine. Yes modern engines are built to finer tolerances as those of old, but taking it a little easy for the first few thousand miles, and even in daily use letting it warm up before really giving it the beans and letting it cool down really pays off in longevity of the components.
Running probably makes no difference for the first few thousand rounds, or with a car the first 70 or 100,000 miles. The reward comes later in life when the barrel still gives good accuracy after several thousand rounds with no sign of needing a barrel change or the car is going strong after 150,000 or 170,000 miles with just normal servicing and is giving pretty much free motoring.