I think it's because they know that people still think it's all a myth and children's stories. They probably figure that Cersei could take it as a ploy to get her to lay down their arms and send her men elsewhere to make her vulnerable, and that she would need some convincing. And clearly the war with Dany is more important to her than one against an enemy people don't believe in. It's not too much of a reach.
They could've taken other measures first though of course. Such as trying to work through Sam to convince the Maesters (and you know, getting the maester at Winterfell to help convince the rest of them), or even see how Cersei feels before setting up a zombie exhibit right off the bat. Work some solutions that don't require a suicide mission.
Stupid accelerated timeline. It's exciting but has its downfalls as well..
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