Problem with that has always been the cost (financial and readiness: the last Lightning team (Firebirds, IIRC) gave way to the Yellowjacks/Reds because as well as the cost of using a Mach 2 fighter for aero displays, 56 Sqn had to devote an awful lot of time for training for the displays.
By all accounts (although I don't knwo how accurate they are) the then AOC-in-C Fighter Command was fairly firm in expressing the view that his squadrons should be ready to defend UK airspace rather than thrilling crowds.
While equpping the Reds with Typhoons would overcome the issue of taking a squadron (or part thereof) out of the front line, the cost would probably be too great (unless Eurofighter GBmH could be persuaded to assist with some of the costs out of their advertising budget!). Also, I assume that there would be issues about converting onto type for those who'd never flown Typhoon before - whereas they've all flown Hawk at some point?