Unfortunately you're quite wrong on a few points there. It would be very hard to justify Piccadilly is a more important station than Leeds on really all the criteria you give.
It is highly debatable whether Manchester is a more important city than Leeds; if it is, its certainly only a little more important. It has a bigger airport and football team - that's about it. In the retail rankings, as a financial centre, as a legal centre, in population and as a digital centre it is most definitely less important. There are several cities that would rank above it on those merits but notably Leeds ranks above on all of them. We're not only talking numbers here, but noting that the Bank of England's only office outside of London is of course Leeds. That the only top 10 legal firm in the UK not based in London is in Leeds, and so on.
There's also both Network Rail stats and the Office of Rail and Road statistics, both of which inarguably place
Leeds as a significantly busier station than Manchester Piccadilly. Nearly four times as many people use it as York, and Crewe doesn't even make the top 5 in the North West, let alone the country.
Put simply, there is a reason that the Government is prepared to spend many millions on rebuilding the whole of Leeds station to become a mega-hub that will be the biggest station in the UK, while only tacking on new HS2 platforms at Piccadilly. Indeed, Leeds is already the biggest non-London station in England, and the second largest after Edinburgh Waverley.
For the record, my station is Clapham Junction.