Why?
If you're going to London/Birmingham it's faster to change at Warrington Bank Quay.
If you're going to West/North/East Yorkshire or the North East the fast services are being moved to Victoria.
If you're going to South Yorkshire from Chester the fastest journey option is using the Northern service to Stockport (which is supposed become a semi-fast service in December 2017 so will get even faster.)
Metrolink connections to places on the Altrincham/Airport line from Chester would be reached fastest by joining Metrolink at Altrincham opposed to in Manchester.
Metrolink connections to places on the Bury/Rochdale lines would improve by sending Chester services to Victoria.
Salford Quays is the problem Metrolink destination but if it's important then stopping Chester-Victoria trains at Eccles would provide better journey times than going via Piccadilly (as you'd currently need to.)
There's also poorer links to the Eithad Stadium but then are those used much on non-match days?
Which stations on the Airport line would you choose to travel to from Altrincham.
Only a tram nut would use the metrolink to go from Altrincham to the airport.