Maybe this is right in the short term to try and bring passengers in. But the biggest problem the UK has is that everything, absolutely everything, is assessed on its value to London. Not surprising, given a major worldwide city (though personally I think that's more on its past rather than its current or future). For long term success of the UK, the various UK regions need to stand on their own legs.
BHX, and Interchange station, is a gateway to the Midlands and all of the things that brings - the cultural heritage, arts, engineering, motorsport, the Cotswolds, etc. Arguably, its also a gateway to much of Wales.
Of course, you cant land that change overnight - but the long term desire is that e.g. the american tourist who wants to holiday in the UK chooses to fly to Birmingham because they want to spend time in this part of the world. Not that they fly to Heathrow and get a coach up one day to see Shakespeares house as their sole experience of this region.
Don't want to labour it I think we are probably on the same page here on most of this but I would say that London is a major (which may even undersate it a bit) international draw for business and tourism.
I think Birmingham has a competitive offer for inward business vs London, and Manchester for that matter, on the grounds that, it's very conveniently located for the rest of the UK as well as London.
You can't understate the importance of a certain proximity to London to any business operating in the UK due to the massive population imbalance, the fact remains that it is the seat of government and that many UK and international businesses have already chosen London for their UK head offices and that isn't really going to change in a massive way.
The West Midlands conurbation vs London does however have similarly qualified and competent workers to London but it doesn't have London rents (business and residential), London hotel prices, London beer prices, London house prices, London salary weightings etc... I'd further agree that despite being known as an industrial area most places in the West Midlands conurbation are still actually quite close to the countryside and AONB's, as well as having plenty of it's own history sites, top flight sports, shopping and enterainment venues.
That said London clearly has, for the first-time visiting international tourist some bucket list attractions like Buckingham Palace, Big Ben, Tower Bridge and the Houses of Parliament that are very difficult for any city to compete with. With that in mind I am pragmatic and reaslistic about the challenges surrounding promoting Birmingham as a stand alone destination to international tourists, it does however present and excellent entry point to see sites in various parts of the England, including London, if not Great Britain and Northern Ireland.
Personally I don't care about being a stop over point for travellers to London, as Manchester is clearly fine with taking some passengers with Birmingham as an origin and destination and LHR has clearly been benefiting from Birmingham traffic for years.
Regarding the name Midlands gateway, and I'm happy to take stick for this, but this seems quite parochial and along the lines of the long forgotten acronym the area adopted rather than being known as "Greater Birmingham".*
At the end of the day HS2 goes to 4 places, Birmingham City Centre, BHX and 2 London stations, it doesn't even connect directly to the wider network at New St. Whether it is a London gateway or vice versa (I would say it is strictly speaking both) I just see it a the best potential angle to promote the airport and our regional economy to make a big deal about the convenience and proximity to London. I think the fact that LHR is, for all intents and purposes full, a very relevant argument for the need for extra capacity anyway.
* BTW I am from the West Midlands but definately not an 021er and I would relate the same argument here as West Mids vs Birmingham as I do to London vs Birmingham.
Surprisingly (to us maybe) many people outside of the UK have a limited knowledge of the cities and they may
only know London. Similarly many people outside of the UK recognise the names of cities from premier league football teams, which without making any partizan statement here, maybe favours cities like Liverpool and Manchester for recognition of the names (sharing the same name as the city name). Typically if I'm explaining to an American for example where I am from I will just say Birmingham as I know they are unlikely to understand or appreciate the regional distinction I grew up using. Sometimes they don't know the name Birmingham at all and I often find myself explaining that for convenience as "near London". For an American in particular 100 miles isn't necessarily a long way to travel to an airport by car, even though it takes a lot longer than 35 minutes.