I'm going to say right off the bat that I understand but dislike the three minute delay.

One of the things I thought of that could certainly be possible, especially if you're going to add two new options to the spectator system, I thought it could be a nice option to add a spectate friend option so that fog of war is not visible and only your friend's team is visible so that it can be viewed in real time and you talk and coach your friend in real time without the ability to view the enemy team.
Viewing real time events in skype with a friend would be much more fun than having the playing-friend have to recall what happened three minutes ago to have to laugh at something.

Good suggestion.

I see why you would want this option, but it brings up another balance issue: having more eyes-in-the-sky for a team than usual. If spectators were allowed to look freely around the map (fog of war or not) they would be able to catch incoming ganks and watch hotspots while the players could focus on laning.

Even if spectators were locked to champions, they could watch the minimap and give warnings.

Ideally, for your suggestion, spectators would be locked to players, completely unable to move the camera, and the minimap would be disabled. You could still help with builds and give advice for teamfights but it would be more like having a coach and less like having a lookout.

It's the same thing as a friend standing behind you. That's allowed. Allow this. It makes a lot of sense.