Prairie dog hunting one time I shot 120 rounds of 220 Swift in just a little over an hour. The barrel was h o t .Total round count for the day was around 300. It still shoots just fine and those were hot loads, near 4000 fps.
AR15's...I have shot hundreds of rounds in an hour. Years ago I could kill a case of 1000 in a day.
I'm not saying a barrel can't be harmed by shooting it, it can. But it takes a lot of sustained fire to do it with the modern steels being used today.
And on a side note, there must be something wrong with my Remington 700 Varmint in 220 Swift caliber . When I bought it in 1993 a guy told me that the barrel will be shot out in less than 600 rounds. I have around 3500 through it now and it's still going strong.