Caldendly/cal.com don't compete with/replace CalDAV. They solve different problems. CalDAV is a protocol for exchanging calendar data. Calendly and alternatives are tools to let people outside your organization schedule an appointment with you.

It's a bit rough around the edges, but I made precisely this. You bring your own CalDAV server, and it will create a REST API that allows for scheduling. Alternatively, the CalDAV functionality is separated into a library, so you don't have to use the provided REST endpoints.

The front-end is separate, and I haven't put much love into making it useful for other people. But it does work.

https://github.com/justinrubek/calendar-scheduler

> besides a fancy UI

Well… this…

Not everyone knows about the CalDAV protocol, let alone how to interact with it.

The extreme vast majority of calendar users probably wouldn’t care to learn either.