The Enhanced Insert Template dialog doesn't support setting a custom view as default, and there's no configuration switch to hide the OOB views. The dialog decides what to show based on what's accessible to the user's security role — you don't get to influence the default view the way you would on a standard grid.
That said, here's what actually works:
Security role + record ownership is the most effective lever. If users only have access to templates owned by their BU, the noise from irrelevant OOB templates naturally disappears. Not perfect, but it's the cleanest supported approach.
Custom views exist on the Email Template entity — you can build one scoped to your templates using a naming convention or a custom category field. Users can switch to it manually inside the dialog. It won't open by default, but once they've used it a couple of times it becomes muscle memory.
If this is the CI Journeys side rather than D365 Sales, the template picker behaves a bit differently — the Asset Library in Journeys gives you more control over what surfaces and for whom. Worth clarifying which context you're in.
The honest answer on hiding OOB views entirely — it's not supported without going into PCF or unsupported form customisation territory, which I wouldn't recommend for something as frequently updated as the email editor.
If the core problem is users landing on the wrong templates and wasting time, the BU ownership route is your best bet without touching code.
