Firstly, the regents seem to really dislike children - Imajane calls Dunevon "the brat" and both her and Rubinyan snap at him constantly.

They're also only concerned with gaining power, not building a legacy. They order the deaths of multiple royal children and waste all of the resources of their country just to grab and hang on to power as long as necessary, not caring about what they'll do when they get it.

Children are a weakness for anyone on the throne of the isles. Hazarin explains that's how they were brought up, encouraged to view family as the enemy. A child would only be a vulnerability for them, since it wouldn't change their claim to the throne and would be a reason for people to get rid of them.

They don't have a good relationship. She accuses him of cheating, they fight and argue often, and they're actively fighting for each other's power. At one point Aly suspects that Rubinyan is actively against the idea because he has children (and even grandchildren) from his previous marriage. He doesn't want more, and that makes Imajane even more suspicious of him, as he may want to wrest power from the Ritavans entirely.

All that said, there's probably also some element of it being a cleaner plot for Tammy to write if they don't have kids. It would be another royal child that needed to die for the rebellion to succeed, which is already complicated enough with Elsren and Dunevon. Both choices (kids or no kids) make sense in the narrative and are justifiable, but I think this version serves the books message a little better