I think I just didn't explain it well enough. A common refrain against unlimited/untracked sick time is that employees will abuse it to be lazy, and the only way to fix that is to either closely monitor/track sick days used, or have a pool.

My point was that if performance is an issue there are ways to address that. And if enough work is getting completed, it doesn't matter how many sick days were taken (so no need to track/have a pool).