My read is that the Sleepless accepted the deal in part because they were desperate.
Rysn made a good point - that now, Akinah had become interesting. The Radiants were trying to get there. Killing this expedition would just emphasize that there was something powerful and interesting there, and they'd be back. Or that would draw the attention of Odium's forces. To the flying radiants, the permanent storm was a big bullseye. The Sleepless' current plan for keeping the Dawnshard protected was now unviable. And they had no other plan.
Until Rysn suggested one.
No, it might not be a permanent one. But it would do for now. For the duration of the Desolation. And it was better than no plan at all.