Fix Summoner Once and For All in 6.0 Please!

[Anhra]

Which makes perfect sense.
Otherwise you'd get a repeat of what happened back in Patch 2.3 and Ramuh EX (as in, you could totally let Titan-Egi tank him.

And currently, a group of 5 SMN are technically capable to outheal any damage E4S can throw since the wings of immortality HoT stacks with itself.

https://m.youtube.com/watch?v=zdDxjXMMWgU

[Exodus-E]

And currently, a group of 5 SMN are technically capable to outheal any damage E4S can throw since the wings of immortality HoT stacks with itself.

https://m.youtube.com/watch?v=zdDxjXMMWgU

Not (quite) the same thing.

Back in Patch 2.3 you could literally let Titan-Egi tank Ramuh EX by itself (no dedicated Tank needed at all).
It was such a glaring "exploit" that the devs' quickly adjusted all the pets so they wouldn't be able to (safely) tank anything as dangerous as an EX trial.

By contrast, that video showcased a party composed of 1 PLD, 1 WAR, 1 DNC and 5 SMNs. And every non-SMN in that party also had healing options.
As for the SMNs there, they all used/had Earthen Armor (the one action you called "generic") and Everlasting Flight (the HoT buff).
The latter being unreliable at best, considering you can only get it once you reach the Firebird Trance part of your rotation (i.e. at the very end of it).

So yeah...

[Grimoire-M]

And currently, a group of 5 SMN are technically capable to outheal any damage E4S can throw since the wings of immortality HoT stacks with itself.

https://m.youtube.com/watch?v=zdDxjXMMWgU

Most of the actually important healing and mitigation work was done by the PLD, WAR, and DNC in that clear. Summoner has good utility but essentially what you're saying with that clear is that that Cure III spam from a WHM is good, as that's essentially what stacking 5 sources of Everlasting Flight equates to in practice. Addle is good too but you rarely need more than one caster to apply it. Most of the damage that would kill a group in this fight can't be addled.