That's not correct. If they are proper nut files they will have a rounded cutting edge.The bottom of the channel may not be completely round. I have heard that's a problem, but even the pro quality files generally don't have round bottoms.
That's true of any tool if you go at it like a bull at a gate. Having a good quality and sharp nut file is going to cut a much smoother slot (smoother slot = less friction and better string to nut contact).Although cutting is slow, I never worry about cutting too deep. Although I have no direct experience, I have read that the good nut files are so good that it's easy to cut the slot too deep.
When cutting a nut slot, there comes a point where you need to stop, check, adjust, repeat. The adjustment stage may only require a very short single direction stroke. Sometimes it only takes a bit of 1200 wet/dry sandpaper to fine tune it.
If you just go like you're sawing firewood, you'll have a problem.