Oh but that would be way too simple wouldn't it...
Yes, it would be too simple! Pages aren't really supposed to work like that. Pages are supposed to be just that, pages with static content. Most normal blog users will have just one blog, not to mention that this set-up is the standard as far as blogs go. IF a person wants to be creative and set up something that will be more complicated than the default, then expect it to be more complicated to set up!
Seriously, the WP developers have made this pretty easy. It could be WAY harder to add this functionality. It is a good thing that WordPress allows you to do some extremely hefty modifications to its post-displaying mechanism, The Loop.
It is comparatively simple using the Category method to display only certain posts. You might have to go out and define your OWN MySql query (talk about more difficult...)
Fortunately, you do have people like myself, who are willing to help you through the customization process for free, and plenty more who can give you more personal help on a professional basis.
To conclude, if you want complicated features, expect to do some complicated set-up. If you don't want to cope with complexity, I would suggest using the default arrangement (i.e. one blog per site)
Thank you for understanding,