I probably shouldn't really try to think about this, because it seens too far off. But it's fun, so anyway:
Maybe they need Jack and Picard because Picard never was connected to Pah-Wraith Goo, and this way they can use a pure Picard sample to seperate the wraith from Jack.
Love it.
Almost certainly not true but it works.
I'm reading other theories on Jack and none of them really hold up - they've done a good job of obfuscating what he is.
Like, the easiest theory is Jack is a successful example of what went wrong with Vadic - i.e. he's a
super-changeling, but was actually successfully controlled by Starfleet/Section 31/etc. - The primary supporting evidence is that he instinctively knows who is a Changeling.
But there are big problems with that - why did Starfleet make him pretend to be Crusher's kid for like, 20+ years (or replace her kid at some point)? And the only supporting evidence has another explanation - he's psychic - and we
know he's definitely psychic, because he puppeteered LaForge this episode.
And that puppeteering style stuff is something usually only godlike beings of various kinds have in Trek.
Of course there's an alternative explanation there too - La Forge is also unknowingly a Changeling, and he used the link!
Part-Borg or "Borg on a molecular level" (whatever that means) is another popular theory, but totally fails to explain the psychic powers and seems very vague.
But that offers a VERY tenuous alternative explanation for the puppeteering - Geordi was also once messed with, with Borg tech - by Lore no less (and a brainwashed Data). So perhaps both Jack and the La Forge kids are "partially Borg" in some weird nanite-related way, because both their dads were messed with by Borg tech? And thus the "psychic powers" are actually the Borg link? He's only mind-read/controlled one of them so far.
Doesn't really explain how he can detect Changelings (maybe he passively emits nanites or something?), though.
(Original theory do not steal lol - absolutely feel free to steal it lol - but I did come up with it!)
Pah-Wraith unfortunately explains everything, but he'll be extremely easy to deal with if it is the case, as Chroniton radiation has been used to get rid of them repeatedly. I still don't believe it though.