I think the biggest problem is that the towns in the West Midlands Conurbation are very insular and do not like to be regarded as one composite area.
There is a lot of truth in that.
As London grew it swallowed up many many villages, but the people who now live in those villages think of themselves as Londoners.
I spent many years in North West London, living in Pinner and Ruislip (villages in their own right many years ago). They were many miles from the London city centre, but we still thought of ourselves as Londoners.
And I am sure people who live way over the East of London, say in West Ham (40 miles from Pinner or Ruislip !), also see themselves as Londoners.
Yet as you say, even though people from outside the West Midlands may see the area (and Birmingham) as one big "lump" the area is in fact made of very discrete areas (towns): Walsall, Dudley, Wolverhampton, West Bromwich and so on.
I am sure the people of Wolverhampton don't say they live in Birmingham, and I live in Solihull and whenever anyone asks where I live I always say Solihull, near Birmingham.
When the West Midlands Combined Authority was set up recently (the "Midlands Engine") their was much opposition from the people of Solihull as they did not want to be part of Birmingham (reinforcing Birmingham's "negative" image).
Personally I think if we are going to complete on the world stage for business and investment we HAVE to see ourselves as one "area".
If you go to China or India and ask for investment for say Walsall or Solihull they will have little idea where they are, go to them as one huge organization representing the whole of the Midlands and you are more likely to succeed.