On a personal level, I don't mind timed dialogues (I really enjoyed Alpha Protocol). That said, they are not without problems.
With Alpha Protocol, I lacked perspective with respect to timed dialogues for things like accessibility, including those that struggle with determining how to respond while hearing the line as it's being delivered, on top of different language support (if you're reading subtitles while hearing non-native voice over and trying to determine what response to make, it can be a challenge).
Some of the criticisms towards our standard dialogue system aren't entirely fair. In terms of engagement, if the player is sitting there thinking about their response for 20 seconds or 20 minutes, they are still engaged in the game. It might be boring for someone watching, but that's not the person we should worry about when designing the game. And while things like animations and so forth are still playing, functionally the player's response still happens within an instant within the game narrative. We could freeze frame everything to drive that point home, but I think it looks less interesting and we're asking for some suspension of disbelief from the game player here too.
In AP it works a bit better as you're supposed to be a quick thinking spy. In TWD it works in large part because the timer is pretty generous (and often prevalent in all of the game systems, not just dialogues).