BHX doesn't have the range of destinations and the frequency of flights.
No disrespect to BHX, but the fact remains that carriers tend to use MAN as a second UK destination rather than BHX (or GLA for that matter). There are only a handful of carriers at, and destinations served from, BHX that are not also at LHR.
HS2 won't change this any more than the motorway system did back in the day.
IF LHR operating at over 100% of capacity becomes untenable, BHX (and others) will be used purely as stepping stone to AMS and KL will be "quids in".
That is the problem in a nutshell: if LHR isn't expanded, traffic goes abroad, not to other UK airports, taking tourism, business, trade and inward investment with it.
It's not a difficult concept to understand!