Because it was not economically feasible to build a new arena solely for the team. The Lighthouse Project was a multi-use approach that would have subsidized the cost of the arena construction with other revenue streams.
There are not a lot of places on Long Island that make sense to build on. A few places over the border in Suffolk County maybe, and the Willets Point area near the new Mets stadium are still possibilities, but this location (next to Hofstra University and the old Rossevelt Field - where Lindbergh took off on his trans-Atlantic flight) is the most central for the team.
And by the way, the owner has spent MANY MILLIONS just on the impact studies over the years.