Neither of those is a good choice. The custom Firefox-only would be a waste of developer resources. Similarly, picking a winner is also a waste of developer resources: there were already extensions that had far more functionality. Firefox should have added a more general "Experience Enhancements" feature that suggested great features that could be enabled and offered a few options. This same concept of periodically offering enhancements to users could be presented periodically and offer any number of things over time.

My complaint is the Mozilla folks missed a more general, better capability they could have built.

I'm sure Mozilla did what they thought was best for themselves at the time.

For me personally, I would prefer most to see it separated from the browser, available as an extension only, so that there is better competition in the extension space, and so the users have the absolute most choice. Barring that, I would prefer to see Mozilla roll their own rather than, as you put it, "pick a winner".

Hard-coding a third party's product into your own is a bad idea; what if Pocket changes their terms of service to be even more user-hostile than it is now? What if they decide to start doing things the Mozilla Foundation can't stomach? Mozilla would then have to go through the same steps again to integrate a different third party, if they decided to keep the same paradigm in place. And I'm not just picking on Pocket, I would be saying the same thing with any proprietary third party service.