On Supergirl, Shelley Island shows up in the fourth season.
Per the Wiki article:
It was converted into an interplanetary port of entry by President Marsdin for alien immigrants, but was shut down and abandoned after Marsdin's resignation.
The symbolism is obvious: a monument resembling the Statue of Liberty, a purpose and name similar to Ellis Island.
However, Ellis Island was used for immigration processing because large numbers of immigrants were coming by boat to New York City from Europe: perhaps even the majority, given a limited number of boat routes. On the other hand, extraterrestrials aren't necessarily aiming for National City, and mostly arrive by spaceship (and thus won't be coming by water). In fact, unless their spaceship landed on the island or in the water, they'd have to be transported out there by boat. In-universe, what's the utility of Shelley Island?