When I saw the title "zero-equity co-founder" I thought it was about inspiring employees to work as committed as an actual co-founder, which would be totally appropriate.

I think the downside of single founder startup is that 1. there's no one to bounce your ideas with; 2. speed to market is greatly reduced; 3. there's no one to share the stress or keep each other motivated when things get tough; and most importantly, 4. there's no one to share the joy when you manage to solve a business/technical problem that is not visible to outsiders.

I don't see any apparent advantage of keeping a single founder startup. You may have the ability to run the startup as well or even better as a multi-cofounder startup and keep all the shares - but it's not fun, and fun is very important for an entrepreneur!