I'm not sure that there is any problem with mixing the types of traffic in question. Years ago, Farnborough would often have very slow aircraft and very fast jets in the circuit together. At Kidlington there would be many Cherokees in the circuit togerth with fast twins joining off instrument approaches.
I have never criticised a fellow controller because I always assume that whatever decision one reached had a good reason. What immediately made me sit up was the decision to instruct the smaller aircraft to go through the ILS and re-position on the right side, but we don't know if there was other traffic behind in the circuit. I assume that the pictures of the radar shown in the AAIB report were from the display in the Tower, hence visible to the Aerodrome Controller, so he should have had a good idea of the relative positions of the two aircraft and of the closing speeds.
Why did he decide to tell the smaller aircraft to go through the final approach rather than a) instruct it to orbit or b) to extend downwind? He must have a reason but we shall never know..
AAIB reports always list in some detail the qualifications and experience of pilots involved, but rarely those of the controllers. In this particular case, it merely says he held an ATC Licence - no information on ratings or validations. Was he a validated radar controller at the unit? If he was, and given the snaps shots in Figs 1, 2 and 3, I am sure that he would have taken different action. I truly feel for him.
Sure it would be extremely useful if all GA aircraft had transponders.... but you know the attitude of many of the clockwork mouse brigade. Hell, many of them don't want radios!