SQLite is literally a backend for MLflow, so the argument being made really is that you should just use SQL when you can, which is kind of adjacent to any criticisms of MLflow
Is querying the underlying SQL database officially supported in MLflow? Last time I used it, it wasn't documented. I took a look at the database and it wasn't end-user friendly.
As someone replied above, it's because SQL is just 1 backend and it's weird to expose an API that only works on 1 backend. Once you have many devs working together, you need a remote server. If you have a remote abstracted backend, it needs to have a unified API surface so the same client can talk to any backend. You might argue "This interface should be SQL", and to that I would say there are many file stores (like your local file system) that are not easy to control with SQL.