If Olav had not come along, what would have happened? Presumably the norwegians would have asked someone else? But who were the likely candidates?
His uncle Prince Valdemar. But he had a Catholic wife and grown children who wouldn't have adjusted so easily. There was also Prince Carl of Sweden before Oscar II fell into the Norwegian trap and declared all Bernadottes out of the running. Maybe Norway would have gone republican after all?
Van der Kiste's
Edward VII's Children says "Names of princes from Greece and Spain were suggested, but in the end the Storting agreed that only somebody from the houses of Sweden or Denmark would be acceptable."
Why did they have only Olav?
Did something bad happen to Queen Maud during or after the birth which made her infertile?
She only had him after seven years of marriage with an adoring husband, and she'd never been pregnant before. 1903 till now has seen a LOT of speculation about whether Haakon or even Maud were his biological parents (I think one of the original theories was that he was supposed to be her unmarried sister Princess Victoria's bastard.)
Anyway, there is decent evidence now that he WAS their child, after all, but she obviously had a very difficult time conceiving him (being the tightest of the tight-lacers couldn't have helped, and what is known is that she seemingly had to go into a clinic in London in order to rest uncorseted in private, at minimum).
Maud's health was not robust, period. Despite being very active and very energetic, she suffered from neuralgia, poor hearing
and poor eyesight, and a few other things besides. I imagine the novelty of Olav and a child and an heir was fine, but she probably didn't want to go through pregnancy and delivery again. Perhaps it wasn't judged good for her health.
Anyway, both of these sets of questions are addressed by Queen Mary's (who was Maud's sister-in-law) Aunt Augusta, who wrote to her niece "Motherdear [Queen Alexandra] will not like it [taking the Norwegian throne] and besides they have only got that one peaky boy."