Every time you pull the trigger, you squirt a flame of 3,000 to 5,000 degrees (Estimates vary wildly, but it’s pretty damned hot.) up your rifle’s barrel. And every time this happens, the barrel melts a little. It’s charred an unattractive black, and cracks and fissures develop at the rear end of the rifling where the flame is most intense. Eventually, the rifling is literally melted away and your rifle no longer shoots the way it once did.
This seems to happen in two stages. The first thing you’ll notice, assuming you’ve kept decent records, that that your groups get bigger. Your minute-of-angle rifle will no longer put three shots into 1.000; it will do 1.200, or 1.250, or something on that order, no matter how carefully you hold.
It’s at this point that competitive shooters of all breeds get new barrels because they need that last little bit of accuracy. Hunters, however, can go on for a long time with a barrel that is no longer a tack driver, but is still accurate enough. If your former minute of angle rifle now shoots an inch and a half, so what, unless you want to shoot animals at 500 yards where that sort of accuracy loss could make a difference.
The exception to this is cartridges that burn huge powder charges in relation to their bore size. A .30-caliber magnum that consumes 75 grains of powder every time you pull the trigger is not going to last nearly as long as a .30/06 which burns 55 grains. It will go quickly. Same with prairie dog guns. One of those can die over a single hunt. When you shoot a barrel hot enough to brand cattle (to steal gun builder John Noveske’s wonderful image) it’s not going to last long.
But why worry? That’s what barrels are for.