Why do I lose access to Lovelace "Overview" if I set a default dashboard?

You can find the explanation to that if you click on your Overview dashboard from the Dashboards panel:

So, that is the intended behaviour. You can use custom-sidebar to add a custom Overview dashboard in the sidebar.

Another thing that you can do with custom-sidebar, is to let your Overview dashboard as the default one but configure default_path to your customised dashboard in your Android phone.