That's an impossibly tall order, especially for a company that's cash-strapped. Sony's still behind on many important features to implement, the developers should be focusing on that (cross-game voice, for instance). They don't have the time and money to be developing browsers, which are actually ridiculously complicated. There's engines out there to fit their needs perfectly.
Again, the management at Sony is dropping the ball here. Their solution not only is pretty shitty (I can't stand the PS3 browser for many reasons), it's far more expensive than the alternatives. They need to man up and use open source code where it makes sense.