You seem to be assuming that everything has to be either Class I or Class II but, as I frequently say/ask, there must surely bbe many electrical items that are not either. Something without exposed-c-ps cannot possibly be Class I, yet may not have "double or reinforced insulation", either, so what are they - 'not allowed', perhaps??
If BA22d bulbs were Class I, that would put an enormous cat amongst the pigeons, since few lampholders have the ability to provide an 'earth' connection,, and pendant lampholders are even exempt from the requirement to have a CPC run to them.