'That investment is then spread around the whole of the UK and we end with a world class hub airport. '
That is the national equivalent of trickle-down economics - the argument used by the wealthy to justify low taxes for them. This is generally recognised as garbage. If you give money to the less well off, they spend it, and the money goes round and round in their community. If you give money to the already rich, it disappears, since they cannot possibly spend it.
So the only way to increase the prosperity of the areas outwith London, is to invest there.
As for transit passengers using a hub airport, their value is mainly, I would have thought, is that they sustain routes which would not be viable on their own. This is vital for places like Iceland - how many routes could it sustain on its own? But I'm not sure how important it is to London. What proportion of LHR PAX are transit?
The trouble is that other countries see enormous airport facilities as sexy. How many third world countries have built fancy terminals rather than looking after their citizens? The idea that airport facilities should be paid for by the users strikes them as bizarre. But it seems quite reasonable to the rest of us.