What is special about the ICAO Caribbean region for VFR climb/descent?
It looks like by default, night VFR isn't allowed in oceanic airspace. The 8-8-5 text you quoted appears to be an exception that does allow night VFR in certain specific Control Areas (CTAs) that are in US airspace.

This is from the US AIP 7.1:


  1. IFR/VFR Operations
  1.1 Flights in oceanic airspace must be conducted under Instrument Flight Rule (IFR) procedures when operating:
  1.1.1 Between sunset and sunrise.
  1.1.2 At or above Flight Level (FL) 055 when operating within the New York, Oakland, and Anchorage Oceanic Flight Information Regions
  (FIRs).
  1.1.3 Above FL180 when operating within the Miami and Houston FIRs and in the San Juan Control Area. Flights between the east coast of
  the U.S., and Bermuda or Caribbean terminals, and traversing the New
  York FIR at or above 5,500 feel MSL should be especially aware of this
  requirement.


1.1.1 essentially says "no night VFR"; 1.1.2 and 1.1.3 say "except in US airspace".

As to why, many countries don't allow night VFR at all and I suspect that it's generally not allowed in oceanic regions to simplify international operations and/or comply with ICAO requirements. Trying to remember which countries allow night VFR as you fly along an international route is probably impractical, especially in the Caribbean. But, since the US does allow night VFR, a VFR climb/descent is possible if the specific airspace in question is US airspace.

(I couldn't find any source on why these rules exist so this is all just my own explanation based on what I could piece together. Someone else may come up with something better.)