Can not select a restart time
The actual reason for it to be grayed out is that a restart must be scheduled by Windows for the option to become available. Quite annoying if you ask me, but that's how it is. You must wait for the next update to trigger this and then go look at the option again before Windows reboots the system.
WHY, did this question show up on the front page of unanswered?
There is one or more of 4 possibilities I can think of.
You were already stuck in a required reboot and the process had already started so it was to late to stop it.
You or someone else configured your group policies to prevent changing it. (hold windows key, press R type gpedit.msc, go to administrative templates->windows components->Windows Updates and make sure there is nothing in there configured that will conflict with what you want to do.
Windows home is preventing it. (to many differences on how updates are handled between every version of windows)
You upgraded via a insider preview license which will does its best to prevent you from changing, deferring or preventing you from stopping updates. (Only fix for that I know of might be expired, you might need to register your product key again.)