That was @OWS. And it works brilliantly (v17.6.39).
Personally, I think dropdown labels and primary/secondary templates are enough. As things currently stand, everything comes up in the primary template, and additional action is required only to switch. The primary template is the default, and only when there are special circumstances do you need to do anything else.
If the selection capability were to be extended any further, there are two obvious options. The first would be to set a default template for every tab. That way, a template created for sales quotes would automatically be used for sales quotes. In my opinion, this option could be marginally useful. But the need for it can be reduced by setting the primary template to be the one most frequently used. You would only need to switch templates in less common situations.
The second option is your idea of setting a template for every document. As I see it, that would be almost as irritating as the former practice of always reverting to the in-built template. You would need to remember to do this for every single transaction entered. Otherwise, you would be prone to accidentally generating improperly formatted documents, such as when emailing a bunch of sales invoices.
Leaving things as they now stand has an additional benefit. It will encourage development of more comprehensive custom templates with conditional tests for those special situations. As a result, users will be nudged towards your original goal of having only one custom template that covers all things. Secondary templates would become truly secondary.