Thanks. It flattered me too much; after a while I'm uncomfortable with that. A long while.
I know what you mean. I'm pointing out that it's a repeated, if not consistent, bit of illogical in Trek time travel stories. It is an unavoidable logical issue when events depart from linear causality in a narrative.
Many writers have exploited the illogic as the very focus and payoff of a narrative. Heinlein, at least twice.*
I think that's why the popularity of branched timelines has grown in Trek fandom and in continuity. Yes, it's vaguely based on quantum something-or-other, but it's popular for the reason that it sort of untangles narrative.
Neither the war universe or the TNG universe was the "real one" - both came into existence simultaneously, one based on a different decision made by Picard. That doesn't make the causality less of a problem, necessarily, but it obviates the need to assign "real" or "original" to one or the other.
Which leads us back to "Couldn't two Picards come back?" and the answer is most likely "Yes, they could."
Confederate Picard might not be motivated to come back to this exact point - he never (that we know) found himself plunged into another branch reality that he felt the need to escape from.
It still doesn't make sense, does it? I just think it makes a little more than assuming that one universe came into being before the other.
I will go lie down, now.
*"By His Bootstraps" and "All You Zombies."