Older small engines....

I have been able to make 40+ years old equipment run even with those flopping around throttle shafts. Those motors are set up way rich enough. Sounds like someone cranked up the idle speed screw to compensate for a problem in the idle fuel circuit.
- If its also hard to start you might want to check the Compression. However on rope-start engines, that doesnt always tell the whole story as they will start on as little as 30psi. I would also do a cylinder Leakage test to be sure the valves were sealing.
-I have learned over the years that, that is where to start. Its almost impossible to tune a small engine if it has mechanical problems. When a customer complains of; it wont idle, or down on power, etc, and doesnt want to pay for these tests, I refuse the job. Better he complains to his friends about a refusal than that I spent X amount of hours, or that he paid X dollars and it still doesnt run right.Sure it might just be a plugged emulsion tube or slow jet.But what if its not? Then I have to charge him for the carb overhaul and still have to do the tests. More money. I just do the C&L tests first. 15 minutes, no big deal.
-Probably should mention also; that a high idle could also be caused by a governor hanging up.
-Also, some equipment is not engineered to have a low idle, because it is rarely required to operate there.Vis-a-vis; almost any engine with a centrifugal clutch, various motorcycles with motorcross carbs,certain cheap brands of lawnmowers, etc.
-Wishing you a simple solution....AJ