Remember when Brian was killed and got replaced by Vinny? That was 10 years ago!
How would the series have changed if Vinny was kept forever? I can't really say much about this, since it's been so long since I've watched the episode, but I can guess Family Guy would've lost a lot of its popularity as time went on. The Brian and Stewie relationship is just so cemented into the show that attempting to replace it would be suicide.