Interesting thougts here. I always wondered too why in seemingly every Superman media, may it bee LnC, Smallville, or the movies it seems that Lara didn't get the equal time to talk and guide her son than Jor-El Get.
Though later Lara was the contact Person for Clark in the movies, obviously because they fired the Jor-El actor.
Well, about building the rocket... In the movies it's made clear that Jor did all the science stuff, while Lara is a Historian, I think. In Smallville, Jor-El is also the scientist and was assisted by his lab tech aprentice Raya instead of Lara.
So it would have made more sense that Lara would have the more time to record the Messages, but well, both that Versions of Jor-El are arrogant Snobs who want Kal to do what they think is wright... so he may didn't gave her the possibility do record something.
As for L&C, it's hard to say. I mean, one of the main Problems of that Simulation ist that Krypton explodes while the message is still recorded. That felt always strange to me, I mean how should Jor and Lara configure the globe and save the Messages there after the planet explodes? I mean they must have survived to do so... So i assume that the Explosion at the end of the message was some sort of Simulation here. Yup, we don't know how the science was shared here, because we found out nearly nothing about this Version of Kal's parents. So the theory that Lara who is running around in the Background of the Messages is the scientist of them is not so far from making sense. Given that this Version of Krypton seemed to be a male-lead Society, this could also Play a role so Lara maybe never got the atention she earned - we don't know. But for that, there is a strange thing called fanfiction...
In case of the movies, it can be refered also to that "Father-Son-Dynamic"-Thing, a lot of People think they wanted to mirror Christian Religion.here.
Interestingly, in the Supergirl TV Show, it's Kara's mother who gets all the Attention (the AI holigram etc.) while her father, though he was the scientist and buld her ship, is rarely mentioned ans seems to be not very important in her life, at lest she often refers only to her mother instead of her parents and we learn nearly nothing about Zor-El. Just a random note here.
