if a duke can't be bothered to appoint a lord, then there's no reason why a lord who gets the region later anyway despite that would want to pay that duke a cut of their taxes.
it's quite simple. there are a load of lands and titles, but no one can get at them. any and all ambitious nobles wanting an estate (that is.. if there are no vacant estates) or a title would wish to do something that'll land themselves a title.
no lord still equal low tax rate, doesn't it?