I'll say that breath weapon can be decent enough, good even, but you have to regard it as an actual part of your build, not just a random bonus thing.
So your basic melee fighter is generally better off ignoring the breath weapon, using it only at an especially opportune moment. A bunch on enemies grouped up in front of you, the kind of moment where an eldritch knight would cast a cone spell like Burning Hands instead of doing a melee combo.
Conversely, one of my runs is a green (poison) dragon caster, on whom I'm putting the gear that makes for a poison build. That staff with a poison spell, the robes for extra poison damage, the gloves where poison damage might give poison status, whatever else I'm not remembering right this second. For that character, the breath weapon isn't just a random racial, it's how I trigger the effects of my poison build equipment in a cone, and without using a spell slot to boot.
I've seen all this gear around for for other elements, especially that gear set for lightning damage and charges.
Do your lightning gear build on a dragonborn with lightning breath.
