@SirFraggle You may want to have a look at this, perhaps it can deepen your understanding.
Please also consider, even if we had k=100.000 and out of those lucky ones, every pool were to make 1 block on average per month. It would be a lot more difficult to reach consensus among 100k participants. As a result, you would have much longer forks on chain that eventually are discarded. As a result, and because Bernoulli still holds, if would happen quite frequently that your pool wins a block after 6 months of waiting only to find out later, that this block gets discarded because it was on the wrong fork.
I’d say, be careful what you wish for.