Would p2pool have potential scalability issues if adopted on a scale much larger than now? For example, would the coinbase transaction be a problem with potentially tens of thousands of payout addresses? Also, if the solution to that issue is increasing p2pool share difficulty, isn't that just re-inventing something like solo mining in the long term?
You got it. You can only split a block so many ways. Or more correctly there is an upper bound on the number of p2pool shares per block because shares are added to a sharechain. That means there is a lower limit on share difficulty.
If there were no pools today and p2pool had 100% of the hashpower directed at it, then with 1 share per second the p2pool share difficulty 1/600th of the block difficulty and there would be on average 600 shares found per block.