You yourself referred to proof rounds. Every proof house has a protocol, for example, 40%over max for three rounds, followed by examining certain points of barrel and action for damage. If those boxes can all be checked as passing, the gun passes, and you are never to fire proof rounds again. That is one of the ways of saying "occasional use". Three times over the life of that firearm.
Every time a firearm is fired, there are a lot of places that are stretched or flexed, and they return to original condition. If the loads exceed the intended pressure levels, that normal flex is exceeded. A piece of steel that is stretched too hard will begin to wrap, or permanently lengthen. The steel can undergo many kinds of breakdown. After hundreds or thousands of over pressure loads, that firearm is going to have serious fatigue in several places. It may show with the barrel or receiver cracking, or the bolt lugs flattering. A revolver may become misaligned, the top strap ma stretche, the cylinder may blow out because of the steel breaking down after bulging outward hundreds of times. There's no fixed means of how a gun breaks down.
In fact, pressures are now measured using strain gauges. These films are attached to a barrel, and an electric current is passed through, and the gauge measures the temporary deformation of the steel when fired.
What do they mean by occasional use? This is what they mean.
"This pistol has been designed for standard ammo and will last forever with standard loads. It is capable of using pp loads, but it is not designed for it or strong enough, and it will not survive forever if you use other than standard ammo. So go ahead, you can use pp ammo sometimes, but we'd have to be complete idiots to tell you how many you can safely use."
If I owned a pistol from a good company marked for "occasional" PP rounds, I'd use no more than a box a year or so. A few to sight check, and then carry with them. If I used five or ten boxes a year, I'd be worried about wearing out the resilience of the materials.
I've already told you about an old man who damaged a wartime Smith with PP ammo. It happens.