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Mmh... let's think in a world where there is no longer any block reward.
Why would the total fees go to zero?
Miners would add as much transactions as they can, adding highest fee transactions first. So I don't see how you end up with "there is no more incentive for the POW".
Why would anyone pay a fee with an unlimited blocksize? Where is the economic scarcity?
Edit: What one gets is either a race to the bottom if there is real competition among miners or a cartel that may support fees for a while.
Well, one would pay a fee to get his transaction included in a block. Miners won't include non fee paying transactions, they won't consume their resources for nothing.
It seems you are assuming that competition will drive the price (of a transaction) below miners' costs. Which makes no economics sense. Price will stay above costs, even in a very competitive environment.