If by "homegrown" you mean developed by the club (i.e. they played for the club between the ages of say 16 and 18) but regardless of nationality then I totally support that. Of course, I am biased because at Arsenal we have a number of such players and more coming through.
But you can't do it by nationality, not in Europe.
I don't support propping up bad players just because they've got the right passport. Competition is what makes players better. Even David Bentley agrees on that point.