The F train to Coney Island is actually
three track for a portion of the route, IIRC. (So are many of the above-ground sections on the numbered lines, especially the 7.)
But more generally, I don't think that 4-track is quite the pancaea you suggest. In fact, they've been moving towards "FastTrack" repairs which involve a total shutdown of a line overnight or over a weekend. The MTA likes it. It's faster and cheaper and less dangerous for the crews involved. The thing that makes it not-so-disruptive, though, is that the NYC subway is massively redundant: if the Second Avenue Subway is closed you can take the Lexington Avenue Line which is a block and a half away (Lexington = 3.5th Avenue). Four-track service has nothing on this.
Of course, building it as 4 tracks should have been eminently feasible on the budget and timeline the city has , but the ways that NYC finds to waste money and not-make-stuff-happen are legion and run the gamut from transit to education and beyond...