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.
You don't have to live in an idyllic world of Noble Savages to be better off than most Native Americans are in the US today.