I always thought that it was MOTU's job not only to bring packages into the universe repository but also make them available in the Ubuntu Software Center. There are many stable releases of applications out there, but many of them are not in the Center.
Is it part of MOTU's job to bring that "some" packages into Ubuntu Software Center?
No, MOTU's jobs aren't to just randomly pull in packages from Launchpad, though it's possible for anyone to file a request for something to be packaged, but that could be hit or miss, depending on who is around to do the work and if it interests them (remember a great portion of Ubuntu developers are volunteers).
If you want something to be put into the software center for an existing stable release (not universe) then the best thing you can do is to ask the makers of the software to check out My Apps and submit their application to the Software Center directly. This also has it's drawbacks, namely an application might sit in a queue waiting review (depending on volunteer contributions), or it might sail through relatively quickly, there's really no way to tell offhand.
Either way currently has a problem of being blocked on humans to review things, which as you can probably tell, doesn't scale, here are some blueprints of plans Ubuntu plans on implementing to make this process suck less: