Companies around the whole of the UK benefit as suppliers and we end up with a new piece of infrastructure and most of the money back into our economy. This is why countries like to build during a recession.
This principle would also work for construction of a new transpennine motorway running westwards from Sheffield, a new-build railway terminus to replace the horribly-constrained Liverpool Lime Street, and of course the "indefinitely paused" Transpennine rail upgrades. But there is no sign of these getting funded.
Clutching at straws springs to mind now
In the case of the LHR R3 financing proposals we're clutching at mature oak trees.
spotters concerned about losing new types from the regionals
Aha ... so you actually believe that an extended LHR will suck business away from regional airports (although you phrase it in disparaging terms). Well that would be great for regional economies, wouldn't it? Is that an example of 'trickleup'?
those in the north with a huge chip on their shoulder about investment in the nations capital.
A chip on the shoulder ... yes, we can dismiss all pesky objections from the regions with that put-down. Except that those provincial folks pay taxes at exactly the same rates as Londoners. And they're 70%+ of the UK population. And whilst very few resent recent national investment on Crossrail, HS1, Channel Tunnel, M25, assorted LTU extensions / upgrades, Docklands Transformation, DLR, Olympic Villages, Thameslink Renaissance, London Terminal Stations Rebuilds and so much more, they do now feel that the time has come for a little public investment to come their way. Is that a really a 'chip on the shoulder' or is it a valid aspiration by any reasonable measure?
Remember that all your arguments about major infrastructure projects creating employment opportunities and wealth across a wider spectrum apply equally to initiatives located in the regions. The difference is that they've been waiting 30 years (and counting) for their turn.