Here in Norway, the long-distance trains have reserved seating: Oslo-Trondheim, Oslo-Stavanger, Oslo-Bergen, Trondheim-Bodø. And a few of the shorter-distance trains that are infrequent or otherwise special (Raumabanen to Åndalsnes, for example). All the seats are reserved. No special charge; you go online or to a machine and you pick your seat from a diagram of the available cars. I think the conductor has the manifest on his-her electronic device, too, because I have seen them look up people who lost their tickets. Try choosing a seat here:
https://www.nsb.no/en/frontpage" onclick="window.open(this.href);return false;. Put in one of the long-distance city pairs, choose a train, and choose your seat. On the shorter-distance trains -- ones that go maybe two hours or less -- as from Oslo S to Halden, Oslo S to Lillehammer, etc., the normal seats are not reserved but the NSB Comfort seats (read Business Class) are reserved.
There are no signs on the seats themselves, except the numbers. Most people board with tickets. Many buy them on their phones or computers and get seats assigned that way; many buy from machines and I know they get seats assigned. The few who get on the long-distance trains and need to buy a ticket talk to the conductor who directs them to a seat, as near as I can tell.
Amtrak should definitely NOT go to the system of selling reserved seats for an extra charge and indicating those seats somehow on board. Amtrak should just make all the seats reserved. Maybe Norwegian or Japanese trains arent FRA legal, but Norwegian or Japanese seating software should be fine off the shelf. Or, for that matter, Chilean long-distance bus seat reservation software. Make the reservation an automatic part of buying the ticket -- letting whoever wants to choose their seat and assigning the rest at random -- so that everyone who has a ticket has a seat.
The harder question is whether/how to restrict passenger choice of seats to ensure that you don't get situations where the train is never more than 70% full but there are no seats available from the originating station to the terminal station because every seat has been reserved for at least one segment somewhere along the way. Maybe you allow people to reserve seats together and window or aisle, but save the ability to fiddle the exact locations around a day or two before the trains leave? Or do you just have zones assigned to the most common trips, with software to adjust the zones (ie offer different cars or groups of seats) to match changing demand? Maybe they do that here in Norway, come to think of it. When I booked from Oslo towards Trondheim a while back I don't think I was offered the whole train to choose from. There were eight cars: two sets of four connected cars; impossible to pass between the two sets. Each set has about half a car of comfort, one family car, and the rest coach. I am pretty sure I was only shown two cars to choose from in coach, even though there were more like five coaches. Someone, somewhere, probably has mostly solved this software problem.
