I just want to point out that the railroad reservation bureaus has no trouble assigning seats in advance, including the ability to group people in the car where they got off if was at a small station with a short platform where not all doors opened (which was usually accomplished using a "shorts" coach).
This systems were typically manual and depended on clerks maintaining a series of car seating charts, but it worked. Reserved seating was generally a feature only of premier trains and the railroads did charge a surcharge for reserved seats.
Those systems ceased being used prior to Arrow when Amtrak moved from continuing to use host railroad reservation bureaus and established their own centralized reservations, which was pretty early on. I do recall a period after Amtrak established their own central reservations but before Arrow when on the Coast Starlight, at least, I was assigned to a car in advance but not a seat.
There is really nothing precluding re-establishing a computerized version of such a system, other than possibly the limitations of Arrow itself. The single variable that might be missing is the stations at which a particular car line is opened. You have that, and the reservation system which can assign people to the correct cars.