The UK won't exchange licences without a reciprocal agreement
Which, as I have noted before, shows that the British government stance has almost nothing to do with supposed road safety and everything to do with politics.
Would it hurt them to at least provide a few concessions instead of treating experienced American drivers like complete novices?
It seems that at present the list for "direct swap" licenses comprises Australia, Barbados, British Virgin Islands, Canada, Falkland Islands, Faroe Islands, Hong Kong, Japan, Monaco, New Zealand, Republic of Korea, Singapore, South Africa, Switzerland and Zimbabwe, plus Jersey, Guernsey, the Isle of Man, and Gibraltar.
EU countries are all included because of EU regulations rather than direct reciprocal negotiations. In fact EU license holders are not even obliged to swap a license at all and can continue to use their foreign license beyond the 12-month limit which applies to others.