Couple months ago, on Swiss Rail, they offer guaranteed seat assignment for 5 Francs which is about 5 USD. You can select your own seat and when you board, there is a small LCD sign above your seat, same location that Amtrak puts those colored seat checks, that says it is "Reserved." In the UK, there was no extra charge for reserving an assigned seat but what they do is put a "reserved" seat check with starting and ending destination on your seat.
I'd love to see something like this on the corridor services as well. It can be a big source of extra revenue per train especially busy ones. The current hurry up and wait system just makes the system less pleasing.
While the idea of seat assignments has merit, actually permitting passengers to select their own seats won't work on Amtrak without (perhaps severely) reducing the capacity of the train. There is far too much traffic to/from intermediate points for this to ever be practical; You would end up with situations where there are plenty of empty seats available, but no one single seat for the entire duration of the passengers' trip. Of course, you could permit people to make a 'forced choice' of several available seats, taking into consideration already existing reservations
Not understanding how it won't work? The majority of the trains already have reserved coach seating. Unless they are overselling, which is Amtrak's problem, in theory your guaranteed a seat, meaning there is a seat already somewhere on the train designated for you. Even if you buy a ticket somewhere intermediate, in theory they are only selling you a ticket for an available seat between where you are getting on and the final destination.