That's kind of what happens now (loading screens), but the problem is that console hardware is designed to barely pull off and play acceptable games and no more. From what I remember, the Xbox 360 was originally designed with 256 MB of RAM, but got bumped to 512. Games up until a few years ago had to deal with that. Many games go through many build cycles of simply optimizing RAM usage. When you have more demands on RAM during gameplay, there isn't any left over to load future levels. Add in that many games today are open world, and you don't know where the player is going to be, it's not worth it. Even PC exclusive games don't have this feature.
I imagine with some filesystem trickery you could even do it without the game even knowing, it just magically gets everything it asks for virtually instantly.
Console hardware is almost always sold at a loss. No company would build a console full of RAM (no matter how cheap it is) with almost no load times. Most people (having acclimated to loading screens) would rather buy the cheaper "good enough" alternative.
They seem to care about loading times....