Or if it's a drone that's backing up the ganger, it won't be intimidated either, right?
So if one specific rationale doesn't make sense, then obviously you don't use it in that circumstance. Maybe instead of being intimidated, the opposition is instead being overly cautions in light of your demonstrated prowess. Maybe it's you who's benefiting from uplifted morale rather than them who are demoralized.
Maybe a sports analogy might work?
If your football team demonstrates a powerful running attack, the defense stacks the line to do something about it. You haven't yet demonstrated a devastating passing attack, but because they're shifting defense to compensate for your success on the ground now you have wide open recievers for a long strike. Being good at one thing ended up giving you an advantage in another thing.
And again, if the GM doesn't feel like unspent edge should carry over from dispatching the mooks to when the Boss steps into the fray, then it can be a "new" fight and edge resets. No problem anymore.
There will always be ways to describe a cup as half empty. It's more fun to describe it as half full, imo.