As long as this remains cleanly open, I'm not sure why you wouldn't run this if you want to self-host. I'm not sure how this will, or won't play out for Elastic company though. I'm thinking AGPL for server, and MIT for client libraries is probably the best way to go for someone starting any kind of *Server project.

Open-Core as a business model isn't something that the likes of AWS, Azure or GCP can really tolerate if they want to integrate SaaS that the customers want. DBaaS in particular is one of the bigger advantages of cloud providers in general.

Discloser: A family member of mine does work for Elastic, but I have no knowledge of their internal practices or policies or reaction to this.