As
Peter0124 says above, Avanti stopped in Piccadilly platforms 13/14 back in 2019, but it was a mess.
Platforms were overcrowded and (for other reasons) trains ran late also.
My only time over the Ordsall Chord I came from Victoria, saw the Pendolino from Glasgow waiting in the traffic jam at Castlefield Junction to follow us in due course, got off at Piccadilly and got as far away as I could from the scrum at platform 13, caught a Pendolino from the main station instead, saw the Glasgow Pendolino arriving as we were leaving, it then followed us in due course and I caught it from Stockport to Wilmslow. Where I didn't even bother trying to find a seat.
And the Glasgow service became the xx.55 from Piccadilly with the usual calls, hence why I eventually caught it at Stockport. But anyone having a reservation for it had to put up with platform 13 and the train's significant delay.
I think the Stockport calls used to be for traincrew purposes, presumably now they're not necessary and the crew can work the train Preston-Crewe. As long as there are enough "normal" trains then it makes sense to avoid stopping anywhere.