The high speed governors likely saved thousands of saws from burning up. Homelite started to add those setups to help folks from running them too lean on the top. The governor is not like a typical ball/spring check found in the oiler system and does not activate through typical vacuum. It operates on an inherent threshold resonance frequency. Once the saw vibrates at the resonance of that “check”, it opens and dumps fuel. This works to moderate the RPM independent of the H needle. If it is malfunctioning and/or stuck open it could dump fuel regardless of rpm. This could explain some tuning symptoms. I tend to block them off with a disc from a soda can or 2-3 layers of spent diaphragm. Easy to eliminate the governor and eliminate that source of fuel. The saw tunes fine without them. If you run them with a heathy burble, they clean up in the cut and you’ve got fresh plumbing/seals/gaskets they are somewhat redundant.
Tilly had variations of the setup on the 151 in other carbs. With those carbs, there are two means to eliminate excessive RPM. Ones I run that have the additional high speed check, are happy at 1/8 - 3/16 open on the H and a blocked off governor. They still run fat enough to keep them in the happily safe zone. And it helps to keep the fuel from boiling like crazy on those hotter days.
Pioneer had similar setups on some of their 3xxx muscle saws where the H needle could be seated or just cracked depending on load/bar length. Same idea…keep saws from burning up.