Isn't having a doge as a vassal already a struggle? (when your realm is weak, of course, not even Venice could challenge a united and powerful BYZ)
Other than this, Republics already seem to get free coastal city CBs, so the struggle you envision already is possible. Except if you envision some sort of less closely tied vassal republics like the vassal states in EUIII, or puppet states in HoI. I'm not really sure they really are needed for the limited purpose you describe - but on the other side, being able to have tributary states without needing to conquer them seems interesting...