This is why I'm hoping they will finally switch to Chrome in Android 5.0 or whatever version is announced at Google I/O (Android/Chrome event). And then they update that Chrome browser every 6 weeks, too. It's not like they couldn't. They can already push all their core apps to automatically update for Android 2.2+.
According to this HTML5 compliance test, the ICS browser scores 230 (out of 450), while Chrome 15 desktop browser scores 342. Why would these browsers have such distant scores if they shared the same browser core? For comparison, the Firefox 8 desktop browser scores 314 and the Firefox 8 mobile browser scores 314.
There are a variety of options that are disabled on the mobile build to save memory and cpu. It's the same core, it just doesn't have all the bells and whistles enabled for a variety of reasons.
It's not Chrome. It's based on WebKit, like Chrome, yes. But it's not Chrome. (Easy way to check: note that the icon says "Browser", not "Chrome", and it isn't the Chrome icon.)