Is it possible to have the template for a new page automatically be selected based on the fieldset being used?

For example, a client using the CP creates a new page. They select the "Long-Form Content" fieldset, and so naturally the associated template should be used. But rather if they selected the "Collection Gallery" fieldset, then they'd want that template selected.

As it is, so far as I understand it, there'd either need to be a template field in each fieldset, or the client would have to manually edit the page's YAML file (not ideal).

Any suggestions, or something I missed?