I really haven't seen any 2000 pax "new" ships doing the rounds in the Caribbean.
Most are 4000 +. then there are the "barefoot" ones that have 300 passengers. Which would be more likely. Seems the cruise line industry is going for quantity of passengers or Oasis, Harmony, Allure of the seas.

Doing a little research the 2000 passenger ships are around 30 years old ( Horizon, Zenith) which aren't getting good reviews for the age and needed upgraded. Ironically I remember when these ships were new ( last month cruise # 17 for me)

The new large scale ships a booking can be $600 for the week so I don't know if the older ships can compete.

Interesting how this will play out.

Wendell