The problem is that there isn’t an unlimited supply, in this case of time.  The generator that accepts every transaction is not going to be 100% of the blocks generated, therefore there will be transactions that don’t’ get accepted in every block (i.e. low fee ones).  What people are paying for isn’t ‘to be included’ (where they are included anyway in the long run), but rather to be included more reliably in the next block(s).