Natural convection reactors have been around for almost 30 years in Navel service. Why this technology hasn't been incorporated into civilian use is mind boggling... It takes out the biggest risk associated with operating nuclear reactors. The coolant feed pumps are no longer necessary, and the flow of water through the reactor vessel never stops. Which means a melt is impossible unless outside forces come into play...
There are a few key reasons why the currently operating reactors do not use natural circulation:
#1 All operating civilian designs are older than 30 years. All operating reactors are based on designs of the naval reactors of their generation.
#2 The commercial nuclear industry does not have quite the same latitude that naval reactors do in terms of cost or construction. The gigantic capacity of a commercial reactor in comparison to naval reactors means the pressure vessel has to be extremely large and designed for natural convection. As you probably know, the commercial fuel is limited by law to low enrichment Uranium (unlike the naval fuel using highly enriched Uranium), which causes the fuel to be longer and larger, which increases pressure losses thru the fuel, which inhibits natural circulation. There is also not a lot of experience with natural convection on this scale. Sometimes it's be cheaper and easier to go with proven design and systems. Some designers have chosen that path.
#3 Even naval reactors still require a heat sink. Luckily, naval reactors during operation are surrounded by one! Civilian reactors don't have this luxury. Therefore, extensive active and/or passive safety systems are required for their application.
FYI the only major next generation civilian reactor design that does not have natural circulation as a passive safety feature is the EPR. Both the AP1000 and ESBWR tout this feature.
Really, the designs of the current naval and civilian reactor designs are probably more similar than you think.