The reason I say "not for public transport operations" rather than "PPL/IR" is so that a CPL holder, or indeed an FI could hold one. In the case of an FI, they *should* have some sort of instrument qualification for safety but what you find in the UK is that many of them get the IR and a year later let it lapse until they get into the Boeing - something quite rare in the USA where the majority of FI's also have an IR (I don't know any without). A CPL holder who, for example, does stuff like aerial photography, aircraft deliveries etc. and doesn't normally need a full IR, should probably hold some sort of IQ in case the !!!!! hits the fan.
A EIR with precision approach capability would be perfect in these cases.