On the topic of cross-browser code, its a great ideal, and I don't think its beyond workable, even if its painful -- but, on the other hand, you can side-step most of it if you can simply accept not running on absolutely every browser. In that case, you are simply saying "Browser X is effectively my game client application". I think that's mostly fine, millions of people will already have your game client, your game client is probably already white-listed in most school/work environments (whether people should be playing in those locations is up to them to decide when and when its not appropriate), and for someone that really want's to play your game, what difference, really, does it make whether they download a proprietary client or a specific browser? When you start looking at issues of security and trust and potential liability, a browser is actually better in many respects for both the developer and the end user.
You still might have to deal with intra-version performance regressions or broken features -- it's not a guarantee that new versions contain changes that affect the way your game works, but its common enough you'll probably bump against it from time to time. If you picked Chrome as your target browser, Google tends to be on or near the bleeding edge, and chrome alone accounts for almost 60% of web traffic, so you can probably say conservatively that 50% of web users already have your client installed, which is huge. If you were able to add Mozilla to your list of supported browsers, that's another ~25%. IE, another 10%. And all three of those are working towards merging their desktop and mobile versions over the long term, Google is phasing out their mobile browser to be replaced by mobile Chrome, and IE, although behind the others on features, is already the same codebase across Desktop, Windows RT, and Windows Phone (They're not at feature parity yet, though).
So, yes, its a lot of work to maximize the promised potential of HTML5 today, but even just 50-60 percent of web users as a potential audience is not to be understated -- That's bigger than all of the big app stores and steam combined. Chrome has over 750 million active users; if you could make a dollar from even 1 percent of those users, you'd be a rich man. Easier said than done, of course, but its got the potential. For transparency's sake, Adobe reports that Flash can reach 2 billion users, but that number rolls up essentially all PC and mobile install-base, because those platforms can be targeted by Adobe Air (compiles flash to native apps), so its not people who have Flash Player et all installed.