So long as there's enough time to read our options, I have no problem with time limits. Instead of running with whatever you last highlighted, though, maybe "unpersuasive Shep" could become "indecisive Shep" and the narrative would move on without you? Someone else would make the choice for you or the situation would just keep moving?
I can imagine there would be people pulling "MuteShep" playthroughs, then... eh, just a thought.
In AP the timer moved rather quick. Every dialogue option was of three kinds, reflecting the three "JB's": Jason Bourne (professional), Jack Bauer (aggressive), and James Bond (suave). Dialogue generally ran true to form; I don't recall too many instances of choosing "Professional" and getting something that sounded really aggressive or something. Also, your character was a spy, so it was pretty easy to rationalize anything that sounded a bit out of character as not truly reflecting the PC's state of mind at that time.
Something like what you describe could work. Perhaps instead of just rolling with whatever you last picked, the system could require you to actively choose an option before the timer ran out; if you didn't, then you'd just get a suboptimal "Err ... umm..." option. Is that like what you had in mind?
What does such a thing actually add?
If a player is concerned about their conversations proceeding at a 'natural rhythm,' they can simply pick a choice quickly themselves.
This is the only thing I'll say about this, and it's probably too much already, as the only possible outcome of pursuing this is massive thread derailment. The point is to add a sense of tension to the dialogue sequences, and add to the sense that the stakes are high and time is limited. In the espionage world, pretty much every conversation you have can be pretty high stakes. As I see it, one of the nice things about games is that they enable you to simulate experiences you could not have ordinarily; a conversation timer helps you do that.
As to the whole, "Why not just pick a choice quickly" argument, there are limits to this kind of logic. For instance, why bother having your character take damage at all? If you're concerned with realism and challenge, then just quit the game and reload from an earlier point once you think your character has taken too many hits. But that doesn't really seem like the best way to go. Games are built around rule systems, and rules are constraints on what the player can and can't do. Whether or not a given constraint is justified depends on whether or not it serves the story; I think that in the right circumstances, a conversation timer can do just that.