I think the MTAs woes are unique to the MTA/management of the MTA and not lack of competition. Paris and Madrid have no problem building and operating trains at reasonable costs even though they also operate with no competition.
I'd argue the problem is endemic to large stationary organizations, but some do a better job than others at keeping it at bay.
It's interesting to wonder why. I think one aspect is the degree to which politically powerful are willing to fight it. Famously Stalin actually cared that the Moscow metro worked well, and it did, in a country otherwise crippled by complacent behemoths.
Perhaps the Parisian elite likewise take more pride in having a metro which works OK, are willing to spend more political capital fighting for it. They feel some obligation to keep up with Brussels & Berlin, perhaps that substitutes for competition?
