What happens is that major mining businesses who don't want to just quit, start raising their fee thresholds. This eventually creates a situation where you might only have 10% of total hashing power in pool z and everyone else has moved on to either the high fee pools or the medium fee pools.It's true that pool z gets the fees for everything but they only find 1/10 of the blocks. All users that appreciate speedy transactions will pay more than the minimum and 90% of those blocks do not benefit pool z in any way.
Who has moved on? Miners?
You're confused about how mining and mining pools work. If a pool has N miners (suppose for simplicity all pooled miners have the same hashrate), then it finds on average N*a/D blocks per day, where D is the difficulty and a is a global constant. If the average reward per block is B, the average total reward per day is B*N*a/D, which is distributed among N miners, so each gets B*a/D on average. The only thing that changes between pools is B (based on their inclusion policy), so miners will always go to the pool with a higher B (which is the pool that includes all transactions). The fact that this pool is "only 10% of the total hashing power" has no effect on this.
A smaller pool will have more variance, but since the all-inclusive pool pays the best, there's no reason it should be small.
The end result is that pools which only include high-fee transactions will not be competitive, and 100% of the pooled mining hashrate will be in low-fee pools.
And the point remains that although all pools would be better off if all pools accept only high-fee transactions, no pool would initiate a move to higher threshold (without being part of a cartel) because it will
decrease its own profitability. Which, once again, is called "tragedy of the commons", or "prisoner's dilemma" in the 2-player case.
I find it perfectly possible that all of the different pool classes can be profitable, except perhaps the one that only accepts minimum transactions. I'd imagine that at this stage a very large majority of users want to pay more than the minimum to make sure their transaction is at least in the next couple of blocks. Pool z gets a small share of that action.
It gets a share of that action proportional to its hashrate, like any pool. And in addition it gets a share of the low-fee action.
Not less profitable, more profitable. Imagine if 80% of hashing power simply decided that they've had enough of these free transactions. Their mining hardware costs money, it requires work and they want some profit. Traditional block rewards are a fraction of what they were back in the day. They want to keep mining and supporting the network but it's simply unprofitable.
Now imagine that 80% changing their fee threshold from 0.001 to 0.01, effectively increasing the fees by 10. Now users have a choice, they can either send transactions with a 0.001 fee and wait on average for 50 minutes to be included in a block. Or they can add a 0.01 fee, which is still quite cheap, and make sure that their transaction is in the next block.
Yes, if 80% of hashrate forms a cartel and make an explicit agreement to play hardball, they will increase their profit. But
even after the cartel is formed, members of the cartel are better off if personally they defect from the cartel and start accepting all transactions (unless the cartel enforces it somehow), as well as non-cartel members who will still accept all transactions. The cartel would have to crush competition by rejecting all blocks who do not conform to the cartel. And that is
not a scenario I wish to happen.
It's easy to think that everyone would just mine at the pool that accepts all transactions, because their blocks have the biggest rewards. Fact is that it just doesn't work like that. If everyone did that, we would be back to square one where mining is unprofitable. This is why there will be a sort of profitability index or "difficulty" for each pool, not just mining in general. If too many miners go to a low fee pool, suddenly users are not paying high fees anymore because there is sufficient hashing power in the low fee pools. Thus the profitability of all mining goes down. This is not in the interest of miners so it simply won't happen.
Now I'm sure you haven't read
Prisoner's dilemma and
Tragedy of the commons (the former is clearer, it refers to a 2-player case but the logic is the same). Every miner will act in his own self interest, not in the interest of other miners. Whatever other miners do, the most profitable thing to do is to defect (which in this case means accepting all transactions).
Everyone will do that, and as you correctly state, we will be back to square one where mining is unprofitable. (And it's not necessary that everyone will do that, it's enough that
someone will do that).
This can be resolved
if we change the rules so that the global interest is aligned with everyone's self interest. But this requires a coordinated effort, it doesn't happen spontaneously.