SDTGisAnEvilWolefGenius Children raised without punishments are not raised without negative and aversive consequences of their behaviour.
Random example: say I asked my child (older) to stop playing on the iPad and they didn't listen and argued about it, or something, then I might say "OK, you can't use the iPad for X time". It is a natural consequence that if I cannot trust them to use it within the agreed rules that the privilege will be withdrawn.
Now say I was out somewhere with my child and they misbehaved, I would not say "You're not allowed to use the iPad this weekend" or "I'm taking away your presents". That is punishment. Punishments are unrelated to the 'crime' and are purely aversive - you did something wrong, so now I'll do something unpleasant to you back.
But to answer your question, they cope fine. I never used reward charts or naughty steps or time outs (actually, I have once or twice sent to room, but only at an older age), but they have encountered those systems at nursery and school and adapt fine.
Most of adult life involves consequences rather than punishment anyway. If you don't do your job, you'll lose it. If you don't pay your bills, your credit rating will suffer. If you're crap to people, you'll piss them off and lose friends. If you don't look after your health, you'll end up with negative consequences. There are very few punishments in life, except for criminal behaviour.