So you don't get dirt in the case when you pull the cylinder. Do you want to finish cleaning that filth up with the cylinder off? Also makes scraping the gasket surface clean a lot easier.
Since the saw had some sort of lean condition you want the clutch and flywheel off to give it a pressure test and be able to see the seals. If the seals fail you already have them exposed.
I ponyed up the $10 years ago and brought a real flywheel puller instead of using one of the various cave man methods, I don't regret it. Soft nylon rope works fine for a piston stop.
I do nice clean work on my saws........
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