If they ever find a way to fund this new Trans-Hudson tunnel into Penn, there is really no reason to spend all the money for a new route and a new bridge across the Hudson River by the Tappan Zee.
By traversing the width of Rockland County, over the Hudson and down the Hudson Line from Tarrytown, the transit time to NYC would be much longer than it's current route. I believe it is only a 30 minute transit time from Suffern to Secaucus in the current route.
The only advantage is that MTA could consolidate operations into one terminal and they wouldn't have to deal with NJT's constant problems.
I think it may be possible that NJ Transit might not be the perfect, infallible organization that most people assume it is.