The reality of the situation is that you don't react to campers, you proactively deal with them by not sprinting through areas you haven't identified as clear..
This is as simple as taking kit like smoke or flashbangs to deal with campers you know exist, prefiring corners, letting other people run through first (so the camper can expose themself when they kill your teammate), or carefully listening for movement sounds and reloads.
If you sprint around a corner into the face of someone already waiting with their sights up pointed directly at you, you dun fucked up. This isn't a game mechanic restricting you, this is you picking the absolute worst time to sprint.
Unfortunately, a faster ready time for light armor would make an already strong light-weight meta even stronger due to bonuses to weapon handling. It essentially counters intelligent defense by making the punishment for bad positioning much less severe on a meta that is already supposed to get their advantage via faster positioning.
Finally, if this is an issue for you in CQB, then there are options that exist for you: Take a laser pointer. Insurgency is nice specifically in the sense that your hipfire bullets go where you want them. There's no absurd cone. Learn to point-shoot so that you don't have to worry about aiming in a pinch as a result of your bad positioning, and save time. You'll still probably be screwed if your opponent is already aiming at you, but careful hipfire has saved my bacon before.
Sprint to get to position or cover faster, and walk when you're near areas that haven't been covered, not the other way around you goof.