the queen is rather young and new to her position... (in my headcanon she has been queen for a couple years, but that is most likely subject to change if we define it otherwise....if we need to define it at all, which for the time being we don't.)
She's also traditionally considered by the general populace to be a divine conduit, a living embodiment of the gods worshiped by Zeta... so she's sort of a sacred figure as well.
She's testing the waters and trying out the limits of her powers and her tastes/kinks, but she is also shouldering the duties of governing the city at the same time...
...and in her explorations, Z doesn't seem to be responding how she would expect him to respond, how most other men respond.
Any considerations about offspring or how exactly the succession line works in Zeta is, at this stage of the game, yet undefined... by which I mean we're not telling you
Whether it is or will become a subject to be explored in game is something that you will have to wait and find out.
Point of order, Zosar (Abrax) was Zaton's mentor, a master/expert/instructor Stalker for the city of Zeta.. not the previous king. He too, served under a Queen (and yes, all queens carry the name Merneith).