The answer is ‘no’, simply bevause the amount of time & money needed to keep these up to date / linked to stock number (what happens if the original stock breaks down & gets replaced say, en-route?!) to is far to much for the number of people that would actually use it! Don’t forget you can reserve with 10mins before departing any station too, so it would only be accurate for the moment you accessed it.
And XC▸ always keep many seats unreserved. Even from the 10 min reservation system
I don't think there would need to be much time and money needed. I can tell you exactly what seats are reserved and where from and to on all
GWR▸ services, and I imagine CrossCountry employees have access to the same information for their trains. Putting that into the public domain would be pretty easy - even if the 10 min system might complicate things a little.
I agree however that it would be of little use to most people. A better system is to give a broad indication of how many seats in each carriage are reserved - I've seen those on some station displays for CrossCountry services.
Even better than that is actual live loading indicators which some operators including Thameslink and GWR are now starting to introduce, though there is fine tuning work to be done and the trains have to be fitted with equipment to provide that information.