That’s not a trope.
In New York, 2/3 of tax revenue is personal income taxes, and about 40% of that revenue is for filers making over $1M. Pretty sure 80% of those filers, which include non-human entities domiciled in NYC, are in the NY Metro and Long Island, depending on how you measure it.
The percentage of tax revenue just from NYC financial services is very significant, and is very volatile. Because it’s difficult to issue general obligation debt, most NY bonds are revenue bonds secured by PIT. So when there’s a market downturn that impacts bonuses, there is a very significant impact on the state balance sheet, as debt service has a higher precedence than government operations.
Buffalo would not turn into Mogadishu without NYC, more like Mississippi with snow. You’d probably see a significant reduction in services, especially Medicaid, child health plus, and schools, and 30-40% increase in property taxes. NYC moderated the impact of western and central New York’s unfortunate rust belt state as industry was wiped out in the 80s and 90s.
With respect to roads, every state or US highway outside of city limits is maintained at state expense. Most counties get state aid for county highways as well. That state revenue isn’t coming Erie county.