You seem to misunderstand how the penalties work out. 95% of the time after a fight happens, both teams get offsetting penalties, and so neither team is at a disadvantage because of the fight alone. There are instances where one team ends up with more penalties after a fight, but it’s usually because of something that happened before the fight and prompted the fight (and should’ve been a penalty anyway)
As the other user commented, instigator is hardly ever actually used.
NHL reffing is… not great most of the time. Despite being a fan of the sport, I would like to see changes that would reduce the future rates of TBI among players. Refs actually enforcing the rules would probably help a bit there.