Way back in the day, when I finished DMC1 that was what I absolutely expected. But, I have to say, I really liked Dante and wanted to see more of him...and still do. As far as "Son of" games, books, etc. they never seem to have the oomph as the father. Yeah, I guess you could say then isn't Dante the son of Sparda and didn't you like him? Yeah, but we started with Dante as the main character and it revolved around him.
Edit: Sorry, I was watching TV and not paying attention to answering the entire question. Would I welcome it more? Yes but many things depend upon that. I would want the game to keep the canon of DMC and Dante intact. I would want the game to be made internally on the MT engine running at 60fps...unless they decided to let P* give it a try. I think that much of a shake it up would be interesting to see where it would go.
http://www.youtube.com/watch?v=hxqCFWQN7Go Skip to about 0:30... Foreshadowing his planned sequels much? Kinda funny how this line never stuck out much in my mind till I found out Kamiya's plans for the series.