The EU in its 'wisdom' has declared a full bike licence needed to drive this 'car'. This came in with implementation of the third European driving licence directive.
My understanding is this was grandfathered everywhere, so if you had a valid licence to drive one before the implementation, you should have one now (19th January 2013).
In the UK, one should get group A with note 79 added when one renews a full car licence with a test date pre 19/1/2013. And this should satisfy any other country in Europe.
Additionally, the UK adopted the derogation that allows anyone over 21 with a valid car licence, to drive a trike but this is not exportable and won't even cover one on a trip to France (say) from the UK.
I think it's the EEA (European Economic Area; EU plus Iceland, Liechtenstein and Norway), i.e. the European driving license covers a couple of more countries. Other than that I agree with you.

Then it's a different matter that for historic reasons the three wheelers are seen as different vehicles in different countries, and in some they can't decide, it seems, at least with the helmet, as in the USA (or they change it quite a bit, to become one vehicle, such as in Australia, I think); and also that we see different demands in other areas, equipment, safety vests etc. The latter is perhaps the important one, together with the helmet.
Surely, with the all new driving license, if you are allowed to drive it, it shouldn't matter where within the EEA (apart from perhaps some differences for some classes, such as age), one would think? But yes, they did a change in January 2013; for example, a Swedish "B" (car license) from before that date covers all trikes from the age of 18; now it's from the age of 21 if more than 15 kW, and then only in Sweden. It is possible all these changes make it easier on an aggregated European level, but it was far easier some decades ago on the national level.
A good question, I think similar has been asked for specific countries, but then for trads. And I interpreted it as equipment etc. (even though the topic is "Helmet regulations ..."

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Here is one page that might answer some questions about driving abroad (Check for example "seat belts", "safety helmet" and "other specific rules").
http://ec.europa.eu/transport/road_safety/going_abroad/index_en.htm