Lucio in no way can support anyone diving the enemy team unless he is there with him. Regardless, his influence is his aoe. Brig can, and does, balance range and proximity.
Lucio’s CC is in no way considered “offensive” outside of Ilios or LT.
Lucio gets outhealed by her while typically putting out less damage (not including barrier damage). While he does more barrier damage, he cannot do anything about anything behind that barrier.
I disagree that she should play back line. I typically play next to tanks but behind corners/walls. She needs to be ready for clutch Bashes etc.
I do agree with you though, DF is easy inspire upkeep.