Picard not liking and not wanting children is a good character trait and it's a disservice to the character to try and undo that in my opinion.
Good thing Jason wasn't a child during the story in question, then?

A person can not want the responsibility and burdens of raising kids, but still be open to the idea of adding adults to one's family.
Anyhow, I recently watched the ep and quite liked it. Here's my review:
Picard S3 wasn't the first time a Trek series featured a final-season encounter between Ol' Baldy and a twenty-something son (played by an actor in his 30s) with an attitude and a rap sheet, the product of a long-ago romance, who is now being pursued by a vengeance-driven enemy from his own past, that he didn't previously know he had. No, before there was Jack Crusher Jr., there was Jason Vigo, in "Bloodlines." As with Picard S3, there's even a joke about Baldy's hair, though this time, it's the old man himself who fires the zinger.
The episode, written by Nick Sagan (yes, son of that Sagan), has a very nicely written and acted scene of Picard and the young man starting to bond. It ultimately chickens out, however, in revealing that Jason Vigo was merely unknowingly genetically tampered with into appearing to be Picard's genetic son. (Even with 24th-century tech, how does that work?! It's also wildly implausible, given all their prior feats of engineering, that Geordi and Data aren't able to prevent the Ferengi villain from snatching Jason off the Enterprise via subspace beaming.) I'm tempted to call this reversal a shame, but it does set up a nicely played and heartfelt scene in which Picard bids Jason farewell, and they share an unspoken acknowledgement that, for a brief moment, they'd started to make a profound connection, which, through no fault or either, the subsequently discovered truth all but extinguished.
Picard and Vigo have a fraction of the screen time later shared by Picard and Jack Crusher, but the dramatic results are pretty much equal. Between "Bloodlines" and Picard S3, therefore, I prefer the earlier, quieter, and much shorter story.
Episode Grade: B
Nailed it!
