bad idea?
Not really, providing a bare-bones browser and augmenting it with different features as required on a per user basis sounds great in principle. Sadly Firefox has strayed rather far from this.
I don't think there's any such thing as a "great" browser (at the moment) ... they all exist with varying degrees of tolerability. Extensible browsers such as Firefox rank a little higher due to the wide range of customisation options available, but suffer the downside of badly written and/or malicious add-ons.
To my mind, Firefox would be far improved by returning to its simplistic roots, spinning out much of the bloat to optional, Mozilla sanctioned add-ons. A small subset of the most popular/beneficial 3rd party add-ons could also be brought into the fold with development overseen by Mozilla such that high standards are maintained.
Add to that a decent system for vetting other add-ons for malciousness allowing publication on the site, anything else can be manually installed by the brave from off-site locations.
Lofty ideals; do I think it'll happen? Nah.