That bridge is a service bridge, but it isn't implausible that it could be adapted for use by pedestrians to visit Ellis Island. It might involve a few $m and an environmental review, but it has been considered before.
However, despite periodic questioning and advocacy for it to be allowed for pedestrians (to decrease the cost of people visiting, and make the island more accessible), the NPS has stated that "an approach by boat is important to the experience". A $19.25 ticket, run by a private ferry company.
Go figure.