How does difficulty have any effect on pooled mining profitability, it is still 10 minutes a block worldwide?

How does difficulty have any effect on pooled mining profitability, it is still 10 minutes a block worldwide?

It seems more like profitability is reduced because there are more miners competing and not because of difficulty. In fact, if more miners join your pool profitability should not be reduced at all, whereas if they join other pools it would be.

If miners join your pool your share is smaller but the pool gathers proportionately more rewards. When miners join other pools the overall blocks solved by your pool is proportionately reduced.

Regardless, as any miner numbers and pool percentages fluctuate it is still 10 minutes a block on average worldwide so, how does increasing difficulty reduce profitability?

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