It sounds even more weird when you have some arbitrary number associated with it.
I don't think it's an arbitrary number at all. It's a very realistic system.
Example: you are wandering some evil wizard's castle. He has 15 sets of guards patrolling, 10 magical beasts wandering his castle, and 5 enslaved ogres wandering the halls doing work. When you hit a random encounter, it's one of these. As you kill them, they are dead. Eventually you kill all 30 potential encounters and there aren't any more.
Now, the OP explained it as a basic system where after X encounters they stop. I think a better system would be one that rolls the random encounter among the 30 or whatever potential possible encounters, and if the encounter has already been defeated no random encounter occurs. So instead of being full random encounters right up until the 30th and then 0, it would be a gradual reduction in encounters until almost never saw any and then nothing after the last one is killed. I like my system more, but maybe the OP wants to keep it simple and easy.
Now, maybe the switch to re-enable encounters is a little unrealistic, but you can justify that in other ways. Perhaps it's not that there is a limit of 30 patrols in the castle (or whatever zone), but it's talk and rumors about your power spreading among the local monster/evil henchmen population such that they actively avoid you as they start to realize you are way too strong for them to defeat. Switching the switch could symbolize the idea that you are actively seeking out the monsters, as opposed to waiting for them to find you. Heck, you could take it a step further and allow use of the switch before the area is "cleared", and it could greatly increase the chance of finding a random encounter, for those players that just want to clear it faster.
Edit:
Instead of being an arbitrary switch in the interface, make it a skill that some (or all) of the potential characters posses, called "hunting" or something. Training it up could make it more effective, a high hunt skill could make it very easy to find monsters and increase chance of surprising them, while a low hunt skill might result in you walking into ambushes half the time as your poor tracking techniques revealed yourself to your quarry.
Dammit, now I want to design a game.