It wouldn't have been 'in' Birmingham, though. Out in unused land by the M42. Get some massive free car parks, a train line out there. There was no sentimental attachment to Wembley once they decided not to incorporate the Towers in the new design. No doubt Wembley is a decent, modern stadium, but nobody can seriously defend the location or road access.
The original Wembley should have had a high quality but lightweight roof built onto the existing structure and been turned into the national football museum. Could either have used the pitch area to creat exhibits within a unique setting (imagine ab hologram playing that shows England's 1966 winning goal ib the actual goalmouth that you could sit ib a stand and watch) or could even have been AstroTurfed and used for games, skills sessions and basically lots of fun for child visitors (and adults) and the exhibits could have been alk round the concourses. People would have flocked to it and the new stadium could have been rightfully built where you said.