There would be no greater supporter of such an idea than myself.
However, the idea that International Cricket or a Sheffield based T20 team, would "pay for its keep" is a pipe dream. It would need several games a year and with the established crop of test venues (Lords, Oval, TB, Edgbaston, Headingley, OT) and the new venues funded by Durham, Hampshire and Glamorgan there just isn't enough International cricket to go around. A City based T20 would have to fit in with the First Class and current structure as there just aren't enough quality players to go around.
It's only chance to be viable, as a Cricket venue, would be to REPLACE Headingley as the home of YCCC and that isn't going to happen any time soon.
The question is, how do you utilise a sports venue for more than a handful of days a year? If anyone ever comes up with a suitable answer they will be richer than JK Rowling.