That's true, however despite having done a very lot of TransPennine journeys in my wheelchair (I live near Leeds/York and my family are in Greater Manchester) I have never had the situation where it has been too crammed to get me on. It's been pretty packed and unpleasantly claustrophobic on occasion, but I have always been able to get on and travel.
So whilst there are doubtless situations where the train is too packed to fit a wheelchair user on, I do not believe that this will be the case for all 12 trains a day, and not for all sections of all 12 trains. So overcrowding wouldn't prevent those trains being used by wheelchair users now, for at least some of them - but running inaccessible trains guarantees those trains can't be used by wheelchair users.
As a side-musing: It's an odd situation for reservations. If a train is crowded and somebody has a seat reservation, the person with the reservation can ask any occupant of the seat to vacate it (assuming reservations haven't been suspended etc etc etc.) I reserve a wheelchair space. But it would be very difficult to say: I've reserved that space, please stand elsewhere - particularly if that would mean one or more people physically having to get off!