Might be a slight oversimplification.
It hasn't had the 'managed decline' smoking gun, although it's had a great deal of the same inequality issues - but at the same time, as with many capital cities, its firmly in the crosshairs for criticism from other parts of the country.
I get what you're saying, and yes it's an oversimplification. But oversimplification is what the media - and a lot of people who consume that media - deals with (see Brexit). When you're the capital city, the seat of government, and plenty of well to do areas and a lot of art and culture and tourism concentrated in the area, criticism from other regions is surely water off a duck's back?
There are a lot of deprived areas in London, but I've felt there was a bit of a disconnect - where it's part of London, but also not exactly London, if you get my meaning?
Liverpool has routinely taken shit off the media, and other regions we might expect to have more solidarity with; where our name seems to have become synonymous with negativity.
If the two cities were people, London could shoot someone on 5th Avenue and walk away from it, whereas Liverpool could get shot in the back for walking suspiciously.