Perhaps he remembered something Spock had said once upon a time "After a time, you may find that having is not so pleasing a thing after all as wanting. It is not logical, but it is often true."
How could Picard remember something Spock said before Picard was born, in a private conversation that went unrecorded?
It may have opened his mind to the possibility of having children but he hardly came out of the Nexus with a burning need to father a child. 9 years pass between Generations & Death in Winter, plenty of time to find someone willing to have a child with him even if it's not Beverly. It seems to me that he wanted Bev more than children.
Picard was hesitant to have children, yes, but at the same time he felt a responsibility to continue the family lineage. People can be complicated and have different, conflicting drives within them at the same time. Indeed, a good deal of
Greater Than the Sum is specifically about that, about Picard wrestling with those conflicting drives: on the one hand, after marrying Beverly he finally feels it's possible for him to continue the family line, but on the other, he's afraid he won't be a good enough father or that his child wouldn't be safe.
And yes, it pretty much did have to be Beverly, not someone else. Come on, we all know how reserved Picard is. Even if he wanted a family, it's not easy for him to open up to people. It would take someone who was really special to him to penetrate that reserve, and it makes sense that it could only be Beverly. Until then, he despaired that he wouldn't be able to carry on the family line, as we saw in
Generations. He just assumed that he wasn't likely to ever find the right woman and settle down. But then he and Beverly finally saw what was right in front of them the whole time, and once they were together, it opened new doors for him.
As for the decision to have Picard and Crusher get married, that's entirely on me. My editor on
Greater Than the Sum, Margaret Clark, asked me to have them conceive a child, but left it up to me to decide whether they'd get married or not. Now, I'm quite the progressive fellow myself, without any particular attachment to so-called traditional marriage (and of course what certain groups tout as "traditional marriage" today is really very different from how marriage was practiced or defined in past centuries), and I've got no problem with characters having children out of wedlock or practicing exotic forms of marriage or what-have-you. But in the case of Picard and Beverly, I decided to go ahead and have them get married because it felt like it was in character for them and had meaning for their relationship. I mean, here are two people who danced around being involved for nearly two decades, including one who has historically been very afraid of emotional commitment; so when they finally committed to each other, I wanted it to be all-out. It showed how seriously Picard took their relationship, that he wanted the symbolic tie of formal marriage to make it clear he wanted it to be permanent. And it matters for Beverly because of the resonances with her first marriage. Both she and Picard have mourned the man who was her husband and his best friend, and the memory of Jack Crusher sort of got in the way of their relationship for a long time. So having Beverly accept Picard into the same role in her life that Jack played symbolizes that they've finally overcome that hurdle, that the memory of Jack brings them together now rather than coming between them.
Or something like that. I'm not sure I really reasoned it out in that detail at the time; it just felt like the right way to go. And I'm saying that as someone who definitely isn't closed to alternative possibilities.