The Finch Staff doesn't have iframes, which is why it's movement pattern is so erratic.
This is where you are simply incorrect, Finches inflict 15 local iframes. However, even if they did inflict shared iframes, their behaviour would not be affected, since they do not move differently after hitting an enemy like Flinx do. They would continue to fly right through the enemy exactly as they do now.
Furthermore. EOL DPS Killtimes are terrible measure of the power of summoner. You want to measure the DPS of the summoner. Use them against the Destroyer.
It still loses there, by an even larger margin too, I might add. Other classes have monstrous AoE options like Life Drain, Nimbus Rod, Crystal Vile Shard, Orange Zapinator, Jester Arrows, Crystal Darts, Bladetongue, Drippler Crippler and Dao of Pow... and all of them are far more impressive against Destroyer than what Summoner can pull off.
Whips have enormous damage falloff when striking multiple enemies, which makes them actually quite poor for Destroyer, where other weapons like the ones I mentioned can hit numerous times for full damage (except Jester Arrows, which have some falloff but not nearly as much as whips).
The minions it has on offer (before Optic Staff, at least) also struggle to maximize the number of segments they can hit per attack. Blades shredding a coiled destroyer is funny, but almost every piercing weapon can do that, and once the boss uncoils they can only hit 2-3 segments at a time, which is much worse than the options other classes have access to.