Crossrail cost 18.8 Billion for a single, albeit admittedly long line. Given Brexit, and the generally poor financial state of the country, something that will only get worse, no way could that sort of money be brought to bear. It also took 14 years to build that line. It would be 2050 at least before anything opened in Brum.
I agree Birmingham desperately needs something like the tube, but it will never happen.
An elevated system like in Chicago would be more likely, but even that would be astronomically expensive.
We don't know, however, what technologically advanced alternatives might arise that would be cheaper.