Historically weren't XC also restricted at Reading due to the turnback platform not being able to hold an 8 car length and now with probably all trains allocated trains south of Reading are stuck at 4 cars.
Checking RTT for yesterday typically only one of the four XC reversals per hour was performed in platform 3, all the other trains using the full length platforms.
That doesn't imply that platform capacity is the governing factor.
When XC first introduced the Voyager the idea was that six coach loco hauled or eight coach HST, once per hour, would be replaced by four or five coach Voyagers, twice per hour, increasing the service frequency and overall number of seats on offer.
For various reasons it didn't quite work out like that but specifically via International and Coventry there were no extra paths available for the greater frequency, resulting in a HST per hour being replaced by just one Voyager almost halving the capacity.
The other Voyager per hour has to run via Solihull consequently I believe it is the via International services that suffer most from the overcrowding.
So the real culprit would appear to be the pathing constraint between New Street and Coventry and the single line stretch from there to Leamington doesn't help either.