If Britain hadn't established colonies in North America, do you think society would still be better off today?
You mean the Native American society? They surely would.
Only if there was a magic force field that kept everybody and everything from the Eastern Hemisphere from coming over here, but since there wasn't I think it's a little hard to say that they would "surely" be better off today if the British hadn't come over. And even with a magic force field it would only be better if you swallow hook, line and sinker the myth of the Noble Savage.