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Let's assume the number of individuals that join mining pools grows by a lot. Let's say we have one mining pool with 50,000 members. The pool is successful and receives a block reward. The next step is to send to each pool member their share.

  1. Is splitting the current 6.25 reward across 50,000 individuals very costly?
  2. Is there a point when splitting the reward across all pool members becomes impractical?
  3. Are there ways to improve the cost of distributing block rewards to the pool members?

I understand the lightning network is always helpful when discussing issues about increasing the number of transactions. But my focus with these questions is that it looks to me like pooled mining adds a large overhead of transactions that are not part of peoples' desire to trade or do the things they want with their bitcoin.

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You don't have one transaction per payee. The splitting of rewards to many recipients can be done in one transaction that pays to hundreds or thousands of pool members. If the number of payees makes the transaction too large then a few extra transactions are needed.

If the amount for each pool member is tiny, the pool can simply keep internal accounts and only pay out when a minimum amount has been earned.

Alternatively the pool can use lightning network as you noted.

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