Northrop managed to develop the M1.3 capable T-38 into the M1.6 capable F-5. Even so, the T-7 appears to feature good acceleration and a high thrust-to-weight ratio so I suspect some aerodynamic refinement should yield significant improvements in speed.
Well the T-38 became the F-5A before it became the far more successful, capable and appreciated F-5E. The E is what made a name for the F-5 and I expect outside of specific BVR performance against a high end threat the F-5 is a better and cheaper aircraft to run intercepts/air policing than a Gripen or T-7.
You can also get rid of the second seat. Remember that the Gripen C is a much heavier aircraft than the T-7 (OEW 6,800 kg vs 5,500 kg) and can comfortably reach Mach 2 with the F404.
No combat configured Gripen has ever flown Mach 2 let alone comfortably getting to that speed. Just review the F-16 Mach 2 thread to see how claimed top speeds translate to speeds with real configurations and actual day to day operations.
Now for who pays the bill, I suspect that either Boeing takes a risk or the USA or Sweden pay for the development. None of the small countries that might be interested could shoulder the cost on their own but IMHO it would be quite competitive for current F-5, F-16 or Gripen operators.
Sweden has no cash to fund this and I don’t think Boeing is interested. The market for light fighters is astonishingly small, already congested and I don’t see how outside of the USAF order they could justify spending likely more than US$ 2 billion to develop and test this variant. Saab tried that already with the Gripen which has had an unsuccessful export career. If Boeing did spend the minimum US$2 billion on the dev and test of the aircraft and made perhaps US$10 million profit on every aircraft they would need to sell 200 before they broke even. There aren't 200 combined FA-50/Hawk 200/M-346FA in service.
I’ll now speak heresy for the board but I see no value or future for the light fighter market. The FA-50, M-346 and Hawk 200s have all been reasonably unsuccessful in replacing the F-5s and MiG-21s of the world as light fighters. When you put the cost of the aircraft and the capabilities they offer up against medium fighters you see why Air Forces spend that little bit more to get a lot more capability or they soldier on with the F-5 etc as the cost of even the new light fighters is unsustainable.
Far more likely that light fighter roles will be subsumed by advancing UCAVs which would be cheaper to acquire and sustain, more flexible in their deployment and easier to train aircrew on.