Two problems exist though, one that to dedicate & presumably refurbish some 323s would lock them into those diagrams & of course Northern might want to make it a premium service and charge more to pay for them. The other problem is that currently many passengers are arriving from further afield than Greater Manchester, & might not take well to the idea of being tipped out at Piccadilly or Victoria having likely already made at least one change on their way into Manchester. And in the case of the latter, being tipped off the train, onto the tram to cross Manchester would add anything up to half an hour more along with the inconvenience of dragging suitcases, kids etc onto said tram isn't going to appeal.
There is a good reason why TPE operate the services that they do, providing what is a relatively new & growing business in getting passengers from further afield to Manchester Airport without having to change trains and/or modes. This is attracting more passengers (and of course more revenue), and as capacity increases with the 397 & 802s that will be operating the bulk of the TPE Airport services more people again will use the, especially as Manchester Airport is expanding & expecting even more passengers.
Some people continue to blame the Airport services for the timetable woes that beset the Castlefield Corridor last May, but just some small tweaks have already vastly improved reliability & once 5 car units become the norm hopefully reduced dwell times through the corridor will lead to further improvements still. Now if only the Minister for Transport could be persuaded to sign off on the Piccadilly / Oxford Road improvements that were meant to go hand-in-hand with the Ordsall Chord build....