Some saws have a clutch covers with lots of chip and dust flow interference. The goal being to allow the chain to clean out as much as possible before going back into the wood. The big loose chips will dump out of the chain as soon as it clears the wood, a lot more will come off as it rounds the clutch. As soon as the chain on the top of the bar enters the kerf it is loading back up with chip and dust before it rounds the bar nose to start the actual cutting again, so allowing the chain to clean off as much as possible will improve the chains efficiency. This is why having a good bit of bar tip exposed is also a good idea if possible, albeit more dangerous.
A good open clutch cover allows for more chip/dust dumping while providing some direction to the chip/dust pile and protection to the operator and equipment. I am not a fan of a simple bar clamp with no clutch cover, makes a lot more mess, a lot more fine dust floating and I like a bit more protection for me and the equipment.
Does not need to be fancy. On the 066 Stihl the knockoff West Coast clutch cover is a good choice. For years I just used a plastic 1129(029-390) cover that I cut up a bit, also worked great. Plus it was free and lightweight.
On the Husqvarna 365/372 I would poke around for a busted one or just grab a knockoff and cut back a bit over the top/front of the chain and up into the clutch area from the bottom. Leave enough to protect yourself from the chain, a saw on the mill is handled differently, really easy to bump that chain area with body parts.
If you are going to run the 372 on a mill, use at least 32:1, make sure to set it upright between passes and blip the throttle a couple times, listen carefully to it as you are milling any significant change in sound needs to be sorted out quickly. Do not bog it down for a long cut and keep it there, let it keep the revs up with a light touch.
Set the idle mixture screw as rich as possible while still maintaining the ability to idle, let it idle between cuts. I am not a fan of running the saw rich while cutting, also not a fan of running them at the very edge of lean as many folks on this website do. Find the happy medium, not so rich as to taste the fuel in the air and not so ridiculously lean as to provide zero “oh, crap” margin on a multiple tankful of fuel cut.