Why aren’t there pedestrian metros in Manhattan...

While there is nothing nearly as extensive as the Path, there are a few isolated underground plazas that each connect to a handful of adjacent high-rise buildings. The ones that immediately spring to mind are the Penn Station complex under Madison Square Garden (and Penn Plaza office building among others), and Grand Central Terminal. I think i've seen others, but I can't remember details.

I don't think they're as commonly thought of as a "I'll use this to walk from point A to point B while avoiding traffic/weather" option, but for people in the connected office buildings, they provide (somewhat overpriced) options for lunch/shopping as well as public-transit access without the need to go outdoors.