So does Alistair, in time. He wakes every time Cullen stirs; waits until his husband has settled back into sleep before joining him there. If they have to move quickly, Alistair knows he can do it on limited sleep. Look at those months in the Fade.

...All right, that's a terrible comparison, but the point stands: he can safely stay awake a little longer than strictly necessary and still be ready to run.

(They will not chain him. Alistair will fight back the combined forces of Ferelden and Orlais all on his own, if it keeps Cullen free.)