There's not really a good reason for Google to make applications they create work outside their own run-time environment - Chrome. Any technical reason they might offer (sparse array performance) is just facetious. They have the technical know-how to solve such problems, but business wise it makes little sense. I use three web browsers for just that reason. Chrome for Google products (YouTube, Gmail, now Inbox, etc.)…
Yes there is. It's the world wide web. An interoperable universal interaction standard. Or it was until Google started pulling an IE6 game. I use Firefox for everything because there is no central motivation to specialise. If a site doesn't work well, it doesn't get my business.
And web browsers absolutely suck at UI for applications. Imagine the man hours and effort that went into building Gmail. It boggles the mind. Who would even want to maintain that?! All for something that could have been created as a native app much easier. There's a lot of reasons that people have gravitated towards apps on phones, but one of them is assuredly that the experience is better than using a web browser.