In short, nobody is breaking web standards, because they didn't submit their changes to a standards body. Because it's not standardized, it doesn't count as breaking standards.
Now, if they did submit to a standards body, and it got approved, it would be standardized. Therefore, it doesn't count as breaking standards.
Hey, if you want every browser to be identical, that's your right. I happen to think that competition among browsers is a good thing, and that means that they'll always be at least a little bit different. Shouldn't it matter which browser you use?
No major browser vendor (in the modern era, at least) wants to break interoperability -- that's the bright line that separates innovation from fragmentation -- and you'll find that each works hard to stay on the right side of that line, often slowing their rate of innovation to do so.
(And no, saying extensions platforms don't count isn't just language-lawyering, as I think you're trying to suggest. Most extensions platforms, particularly ActiveX and old-style Firefox add-ons, are deeply dependent on the host OS or the specific user agent's implementation, or else they operate in contexts that just don't make sense in the web's origin-based security model. I wouldn't go so far as to say it would be impossible to standardize an extensions platform, but standardizing one would necessarily give rise to a separate platform (the extension to the extensions platform) that was host-OS-specific or user-agent-specific. As I said earlier, there are legitimate needs to get stuff done that can't and shouldn't be done on the web, but that don't require abandoning all web technologies. Maybe you're right that the intent of ActiveX was to kill the web. That doesn't mean that it didn't also solve real problems that the web couldn't solve at the time and still can't today.)
Yes, in terms of performance, user interface preferences, features like bookmark syncing, and so on.
But visiting any page should work in any browser. If proprietary extensions get used, then the pages are no longer able to interoperate. You now have a proprietary ecosystem.
If these proprietary extensions catch on, now you're back to the bad old "best viewed in IE6" days.
I'm not sure you're considering the fact that the web ecosystem itself is in competition with other platforms. The counter to your "If proprietary extensions get used" hypothetical is that if they don't get used, the world moves on, getting the job done with fully proprietary and/or platform-specific solutions -- Windows applications, Android apps, etc.
People don't sit back, put their needs on hold, and wait for the web platform to develop and implement new standards. They use available tools. Would you advise them to leave the web ecosystem entirely? Or use the lesser evil of extensions platforms, thereby solving their urgent problems and indirectly providing long-term direction to the web platform's evolution?
Now, if they did submit to a standards body, and it got approved, it would be standardized. Therefore, it doesn't count as breaking standards.