Its not about creating a 'Mini-London', quite the opposite in fact. We've all seen how London has sucked in business & their employees over the decades, and how that growth has put ever increasing pressure on housing, transport & even cost of living. So we don't need another Metropolis, but instead better connectivity between cities & towns in the North, and to encourage new business (more on that in a second) into the region.
In the post-Brexit world, the UK isn't going to be able to rely on the financial sector forever for so much of it's GDP. We will (in my opinion at least) need to once again become innovators, designers, engineers & builders. But we can't do all of that in London, we need to spread out the economic aspirations to all the regions. To achieve that we have to do a number of things, including convincing would-be investors from around the world that the North is capable of hosting the kind of business we might want in future. And part of that is having a modern, and well connected infrastructure (and this doesn't just include the rails by the way) that can make the UK competitive in a very competitive world market.
So having Manchester airport connected to all the areas it serves is some small part in a much bigger picture. Like I said, its an aspiration at this stage, much work is needed in so many areas. But its either that or continue to rely on the financial sector for most of our GDP in an ever more fickle sector, cramming in more & more people into the capital and surrounding area, spending ever greater amounts of money boring more tunnels in the vain hope of keeping all this going whilst the rest of the country slowly rots away.
It doesn't take much digging to start to see the benefits:
https://www.visitbritain.org/northern-tourism-growth-fund
Its a starter for ten, having direct links to countries that are growing economically & have populations becoming more mobile can offer great benefits. I'm not going to trawl around any further because to be honest it should be obvious that greater connectivity can, and does lead to economic growth through business, tourism etc. And frankly to achieve what are really quite modest aspirations compared to the South East could be realised with a fraction of the cost of London's plans, and bring considerable benefits to more people overall.