This is more a question of tight budgets and priorities than old vs. new. The time it takes to build a new line should not grow, unless money is taken from the new project in the same tight budget.

In Madrid, there was already a major subway system, but new construction in recent years quadrupled that. What's more, in the same timeframe, there was money for major upgrades on old lines, too: many stations were lengthened, some tunnels were entirely rebuilt for a wider gauge [cross-section].

As for NY, the lines can't be much older than London or Moscow, can they?

Older than Moscow, more like London or Paris. But, much of the tunnel and track infrastructure is depreciated, ripe for an upgrade, and AFAIK this situation is worse than in Moscow or Paris (but maybe not London).

_{*Lunatic*, n.
One whose delusions are out of fashion.}