In Firefox's case, at least, it's clear that the only motive in doing so would be genuine concern for the safety of their users— Mozilla wouldn't have any incentive to stop people installing extensions that hurt their own business model.

Firefox Marketplace is open source. It's based on Django and you can host your own. Source: https://github.com/mozilla/zamboni

Doubtful. Mozilla has repeatedly gone out of their way to ensure that their services aren't strictly reliant on a centralized source. Firefox Sync allows you to set up your own sync server. Persona allows you to set up your own authentication server. Firefox OS allows you to set up your own first-class app store. Locking down Firefox add-ons in the same manner as Chrome would be highly out-of-character.