Wasn't the problem with Eyes that avoiding the trigger condition makes each planet with one of them play the same? They're always nasty enough that you want to avoid the trigger.
In some cases, you might deem it OK to trigger it temporarily. Like for example, if you are against an ion eye, but have mostly insta-kill immune ships, then maybe you wounld't worry so much about not triggering it, and won't do a "partial retreat" as the number of AI ships goes down (due to you killing them) so you can keep your DPS up.
With different types of eyes, it introduces more cases where you might be willing to "stomach" it.
(Not all though, like the raid eye and the nuke eye, which are so nasty there pretty much is no reason to ever be willing to "stomach" it, which is why I was sort of hoping they are rarer than the other types.)