BG1/2 both had camp encounters, kingmaker has it etc. Putting that in place is probably no problem
"No problem?"
At the moment you can have 5 Origin characters, and 0 to 4 Custom characters at camp. Larian has implied that you'll meet all the origins in EA and have them until the act ends. That's a bunch more people at the camp as well. Plus there will be camp NPC's.
We are talking about at least 14 (probably more) PC's at the camp (and followers but they're non-combat so leave them off for now). That's just on OUR side. In order to make the random encounter worthwhile, there would need to be enough enemies to be a threat. That would be a tremendously long fight.
If you make a special "temporary camp" to limit it to just the 4 PC's in the active party, that's another map, likely with multiple variations for different zones, but that doesn't work because you'll miss out on the long rest camp dialogue critical for forming relationships with other PC's.
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Timers for events are likely the best option, but they'll need to be made clear to the player.
