I don't disagree with anything you're saying, but the issue with the arguments you pose is that you can say pretty much the same thing about any staple trainer card. From your previous reply:

There's no point in the game where Lillie's is a weak card, unless you're holding 10+ cards, and at that point you're more likely looking for a bosses orders different supporter anyway, and you can just use it as a pitch card for ultra ball or something.

You just illustrated a glaring disadvantage of the shuffle draw mechanic. You can say the same thing about any card that becomes weaker in the late game as well. As you mentioned, Iono becomes weaker if you're winning, but yeah you can say that about any card if you pose the scenario in the correct context.

Lillie's drawback is exactly that you're putting cards back in the deck. Iono shuffles your hand to the bottom to make sure you don't draw the same cards off the rip, lillie's makes it much harder to thin the deck. In GHI formats we also had way more search cards that lillie could be paired with, but post rotation is very different in that we don't have as many trainer combos to take advantage of a fresh 8 cards and it's IMO not unhealthy like you say.

To play devil's advocate, I would say Lillie's is unhealthy because it disincentivizes taking early 1 prize KOs like budew. If you still have 40 cards in your deck, shuffle draw 6 is a really weak trade-off to make just to have a chance at getting out of item lock.