The 6 Avenue subway won't close permanently, just temporary to reconstruct it so PATH can go to Grand Central. It is necessary because Grand Central is a major transit hub and it looks like a serviceable extension according to Google Maps. And what other problems are present with the Grand Central extension.
Google maps is the worst possible way to decide what can or cannot be done with a subway, since Google Maps doesn't see underground.
Let's work our way through this. First we have the street. One level below the street we have the PATH tracks, the PATH station, and the Subway station at 34th Street. One level below that we have the Broadway line that crosses 6th Avenue. Then one level below that is the 6th Avenue line. There is no place to move the 6th Avenue line to get it out of the way.
As for other problems, when you get to Grand Central you have the Park Avenue tunnel, the Lexington Avenue line, the #7 line, and the Times Square-GCT tunnel all in the way. If you come up 5th Avenue to 42nd Street, you can't get to GCT because of the #7 & Shuttle. Same with coming up 6th & Madison Ave's. Can't come up Park Avenue because both the Park Ave tunnel and the Lexington Avenue line run under Park Ave. I also believe that there is a water main in the way which can't be moved.
If anything every goes to GCT, and it is a very big IF, it will be a cross town commuter connection between NYP & GCT. PATH isn't going to GCT ever! It's too hard, too costly, and it make no sense to try to get it there.