> Self-hosted SAAS kind of defeats the purpose. The whole point of software as a service is to get rid of the overhead and cost of self hosting.

This is far from universally true.

SAAS for a lot of businesses is about lack of large upfront costs and lock-in.

The theoretic appeal is that instead of negotiating a large (possibly multi-million dollar) deal upfront, you instead pay a monthly or annual rate which includes an agreed upon level of ongoing support and you have the option of terminating the deal at your leisure. This incentivizes the service provider to offer a good enough level of service to try prevent you from dropping them.

In practice it can be more complicated depending on the particular product, for example migrating data between systems of different vendors can be very difficult or possibly even practically impossible, allowing the vendor to effectively lock you in and get away with sub-standard service.

Vendors who offer to manage and handle the hosting of their SAAS products for customers are just providing a feature to make their product more appealing to people looking for that.