Actually the AT is unique in that they collect the tickets in the station before you board. When you check in at the desk, they lift your ticket, give you a seat check (for coach), and your dinner reservation.
Actually, the conductor and assistant conductor did this in the lobby of DEN. All the passengers lined up in the lobby in front of a kind of podium/desk, and as we filed by, they lifted the tickets, gave us seat checks, and then told us to go through the door marked "TO TRAINS."
Don't recall if they actually assigned seats or if it was first-come, first-serve on-board. (I think they did assign them there.)
But it's still not a regular practice anywhere else I've seen on the Amtrak system.