Almost every fixed gear thread I've ever seen you comment in you mention this. Have you ever ridden a fixed gear? I'm not sure why you think a SS training series is relevant to a fixed gear discussion.

Riding SS is nowhere near the same thing as riding fixed. The largest difference is the forced spin that comes with downhill riding. If you really work at it and let the bike push you outside your comfort zone by 15-20+ rpm it's a very good way to improve pedaling mechanics. It forces muscles that don't normally engage to do so for stability. Being able to put down power at 180+ rpm is a useful skill to have.

Just riding along on a fixed gear over flat terrain doesn't help much. Using it as leverage to put yourself into different training areas you wouldn't normally enter is where the usefulness comes from. There's a reason forced-motorpacing on a fixed gear is/was used for Keirin training.

I recently went back to road cycling and racing from a fixed gear and noticed a large improvement in pedaling mechanics, general climbing ability and TTing speed.

Sprint is garbage though. If there is any one truism tied to riding a fixed gear exclusively, it's that it will kill your sprint.