The "proper" version of a language is the one that's most common in current use, and that can absolutely be codified and taught. Consistent teaching of a set of rules keeps the language consistent and intelligible across regions.
And yes, there is no "owner" of English, but there are very influential bodies that establish the rules that are taught in schools. So in a sense, they do define the language because that's what's being taught in schools, and that's what keeps the language consistent.
Your perspective begs the question, if Standard American English is the "proper" language," how did it become the "proper" language when it didn't even exist 200 years ago? The answer is that language is constantly evolving, and by definition there is no "proper" form of any language. The way Americans speak today is different from 50 years ago, which was different from 100 years ago. The idea of a "proper" form of a language existing is usually imposed by a group seeking to subvert or exert control over other groups, outside of the specific use cases I mentioned before, like professional or academic language. Read this
Britain is a world powet and settled in the Americas (among other regions)
Americans gained independence from the British, and cut academic ties
Years go on and American culture evolves separately from the UK
America becomes dominant military and economic force and English becomes essential for international business
American English as codified gets distributed worldwide
The English used today is very similar grammatically to the language used 200 years ago, so despite the Wild West days of the US, I think education has done a pretty good job of keeping the language stable. We obviously get new phrases and idioms as culture evolves, but grammar has remained pretty consistent
Here are the historical major events
~1600 - British as a world power start to make English dominant
starting ~1400, the great vowel shift occurred - English spelling started to get standardized in this period
1066 - Norman conquest - lots of French loan words are introduced to old English
~800 - Viking invasions begin, bringing lots of Norwegian words and simplification of Old English grammar
~450 - Saxon invasion and Germanification of the older pre-English language
Then look at English from the 1700s to today, over ~300 years, we've had very few changes in grammar. I guess thee and thou finally fell out of favor, but there's really not many changes, and that's about as long as the period between any of those major events.