The only place I've found 6* mods to be useful is in Fleet Arena.
By 6*ing my pilots, I can eke out 1 or 2 more points of speed than my opponent with the same g12 pilot can manage. I've done this with my Vader, and now my TIE Advanced always goes first instead of RNG to split the tie. That was the most important toon for me, because it meant that Biggs had Taunt up, which meant that only biggs got target locked, which meant that when the enemy's Slave1 appeared it couldn't use Proton Torpedoes to hit my TIE or TIE Adv behind Biggs' taunt. For a while when RNG went bad I'd get target locked by enemy Vader AND take some serious damage, then Biggs would taunt, then there would be some bashing while I took down the enemy tank (usually also Biggs), then their Slave 1 would show up and finish off my TIE Adv on its first action before I could dispel the buffs. It sucked.
Fleet Arena has moved on since that meta, but when I dropped 6* mods on my Vader I started winning every time because of that tiny +1/+2 speed difference. Even today it matters, because some folks still run Vader in their front-line Fleet Arena squadron.
With Grand Arena I'll probably 6-dot KRU so my TIE Silencer will always go first, since I'm using TIE-S on defense. But I don't care too much about 6-dot mods other than getting the most speed possible on Fleet. Strategy, synergy, and zetas matter a heck of a lot more than whether your mod is 5dot or 6dot. Given the inherent lack of flexibility for 6dot mods - which was the point of the OP - I'm not trying to 6dot anything beyond what I need for certain very specific pilots.