The body of NYC road cyclists train there. It is considered part of the NYC cycling infrastructure, regardless of state. You want to do hill repeats, you go over to Ranger Station.

Plenty of room in CP and PP early in the morning during the week. 6am. I've safely averaged 19mph around CP on the weekend, in the afternoon. You can most easily do that in the wee hours of the morning.

It is done, people do it, and it's plenty safe.

There's a 20+ mile loop around Jamaica Bay.

There's 40+ miles straight North in the Bronx.

There's 50+ miles to Bear Mountain and back.

The largest investment in cycling infrastructure has been made in the NYC Metropolitan area (which includes Jersey...) as far as the USA goes. The 9W corridor may be the most traversed cycling corridor in the USA.

So, To say that an indoor trainer is the only way in NYC is patently untrue given the plain reality of life here.