What you have listed is quite similar to the crossfire format, but just with a stipulation that EVERY player must duel at least once. This leads to activity issues with the tight constraints and we already have some activity issues with wars with little to no constraints. There's no point in restricting ourselves further if we're really restricted with RL stuff already.
As for preventing one player from dueling all the time - just refuse them. Say you'd like to duel someone else for a change or something. You don't have to accept everything.