[AtE] Bicycling in the Post-Apocalypse

[MWnRNC]

I recently got into a discussion about why bicycles aren't more common in post-apocalyptic fiction and I'm curious if the folks around here have any thoughts.

Logistics
My initial thoughts were that bikes would be less useful than draft animals because their parts wouldn't be reproducible at TL 4, whereas a post-apocalyptic subsistence farm would be more self-sufficient. I was also under the impression that after a decade or two, rubber would have all rotted unless carefully stored. However, I am not really knowledgeable about jury-rigged bicycle repair or husbandry.

Utility
Bikes seem like they would be useful for getting around city ruins and perhaps as a makeshift cart you could load your supplies and equipment onto. I tend to think that you can't carry enough while riding one to make it worthwhile as transportation over long distances. Over rough terrain, even a mountain bike doesn't seem to offer too many advantages over something slower and more sure, while a regular bike might just break. You can travel faster than on foot, sure, but would there be a premium on speed after the apocalypse?

Aesthetics
If I'm honest, probably the real reason I see so few bikes in post-apocalyptic fiction is this. Bikes aren't really stable enough for mounted combat, so you can't have cavalry charges or auto-duels. Has anyone seen any depictions of a "cool, rugged" post-apocalyptic bicycle?