I agree with what most of what's been said, especially by Jo and Satins.
I do, though, think that after a procedure, there should be some recovery period where you're in a state of minor pain and serious physical activity (Sprinting, fighting, climbing, etc) could cause complications (Such as a suture splitting, as suggested, and causing you to bleed/more pain), but otherwise you're able to interact. This way you're still not 100% for a bit after a procedure (like 5-10 minutes?) but you're not forced to lay in a bed in a stupor while medical handles the fallout from manhack the main hall gimmick #17. They can send you off with some paracetamol/tramadol.
5-10 Minutes is my initial thought because, as said, we're operating on typically 2 hour rounds. Spending 30-40 minutes in medical is just... not enjoyable for most. So it's something to slow your roll after you've had a surgery- which should be expected- but not enough to keep you away from RP you want to do. Yeah, people might demand high-level painkillers to get back to securing valids, but I think overall it's a net positive to have some period after surgery where you're not in tip-top shape.
If you have a problem with my self-insert say it to my face Jo.