Here's the economist's outlook on the problem: While a new rail link would provide positive returns for society, neither private nor public institutions are properly incentivized to make it happen.
Traffic on the current rail links, two 100 year old tunnels, is at full capacity and will only increase over time. Lawmakers and analysts dispute the cost of building a new tunnel, but it's generally estimated to be in the neighborhood of $10 billion. It will take decades to recoup the investment. This type of massive-scale infrastructure is beyond the scope of any corporation, but not for the simple reason of scale. Consortiums of private institutions can raise massive amounts of money. But can you imagine anyone in the private sector investing in a project that may not earn money for several generations?
More important is that the project would have many positive "externalities," or societal benefits that no owner can capture and charge for. If 100 people need to get from New Jersey to New York City every day, society benefits from them sitting in a single train, rather than 100 automobiles: less pollution and less congestion. But the owner of the train or the tunnel it goes through cannot charge one person for the value of slightly cleaner air. Only a government can internalize the value of clean air for all.
While the government can value something like clean air, it is not good at valuing long term investments. In the same way that corporations are obsessed with daily stock prices and quarterly earnings, politicians are obsessed with monthly poll numbers and biennial elections.