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Firefox DYING is TERRIBLE for the Web
(tilvids.com)
A place to discuss the news and latest developments on the open-source browser Firefox
It's the other way around. Which browser you use is what directly determines whether monopoly and private companies develop the standard you use.
You could write a standard independently of those companies, but then if everyone chooses to use browser engines from companies that don't follow it, what's the point?
If everyone uses a particular browser then whatever that browser implements becomes the standard. It's all about what browser you use.
If what you want is everyone using the same basis, then what you need is to get everyone to use the same browser engine (which is what is happening already).
However, focusing on that is likely to not result in it being "fully open" as long as the popular browsers are not interested in openness (in particular with a MIT-licensed basis that is allowed to be privately altered, extended and corrupted in proprietary forks by those popular browsers who don't have to be "transparent" on what exactly they changed).
If what you want is for it to be "fully open", then you'd want people to be more careful and choose a browser with a "fully open" basis, instead of using whatever is more popular. It's still all about what browser you use.