At least Meadowhall to Sheffield has both good rail and tram links. The Trafford Centre doesn't have either!
Would you be happy if some local rail services out of Sheffield got truncated with the Sheffield end getting a tram running at more frequent intervals instead, which would directly reduce the number of heavy rail routes in and out of Sheffield? That conversion method is how the Manchester system got as big as it is today.
But "directly reduce[ing] the number of heavy rail routes in and out of Manchester" has yielded secondary benfits:
-Without conversion of the Altrincham line, the current use of Manchester Airport via the Castlefield corridor wouldn't be possible (and yes, no need to trot out the usual 'but mid-Cheshire trains now go via Stockport' argument - still a net win on balance all round, until Dec 2008 at least)
-Similarly, conversion of the Oldham loop assists making the Ordsall Chord timetable improvements possible.
As for the other heavy rail conversions:
-Bury was self contained, life expired and in need of total renewal anyway. Might as well be a tram in that case
-Chorlton/Didsbury was long out of use with little if any prospect/requirement for serious return to heavy rail use.
So in your Sheffield example, truncating routes (not that it is the actual plan to do so of course), would benefit other corridors.