Now, sure, there must be plenty of memory-safety issues in GPU drivers, but why find an exploit in a driver only some users have installed, when you can find an exploit in the browser everyone has installed? The GPU driver exploit doesn't give you higher privileges.
WebGL has been around for a long time and the feared exploits never materialized. It's been no worse than other parts of the browser and better than many.
Now POSIX was arguably successful, but it was limited in scope (not including the UI aspect of things). Also: Windows...
Additionally, the absence of that big global state which is the filesystem makes the development of portable applications way more easier. There's always been limitations to what browsers can do, but personally I don't regret iTunes, Outlook or all those desktop app advantageously replaced by SPAs. I can log from any computer/smartphone and I get my apps. No installation process, configuration, the usual missing/corrutped library/dlls, etc.
And the problem of data ownership is not a technical problem. If we didn't have browsers, software companies would have moved those data away from you and have desktop app access them remotely anyway.
I get that abstraction levels suck. But only if the cost/benefits ratio is bad. Java applet had awful UX AND they were slow. Now SPAs can be quite responsive and some of them a pretty cool to use.
It's a goldmine. Think of all the future jailbreak entrypoints this will make possible.