Subcritical experiments are done in underground test sites. US does them 1,000 feet underground inside boreholes in Nevada test site because the explosion releases plutonium. Hiroshima has a Peace "Watch" Tower where they show number of days since last nuclear experiment and they count subcritical tests also.

There is psychological effect, but it's not that important. More important is keeping nuclear test ban in effect. If the US does test, Russia and China will follow.