There are more ways to injure your left hand then you might think
@Paul Bunions . One wrong way is 'slapping' the chainbrake. If the left hand is not thumb- locked and to roll your arm to make the brake you could...and many it seems have...let the left hand toward the chain...perhaps the right hand - on the throttle - gooses the machine... If the left hand gets loose as the machine accelerates, it goes to the chain... then to the ER.
Gloves, are NOT required in FSA except in high level threat situation- judged by the personel- you... any sort of gloves are not specified in OSHA... hold your left hand in front of your face...right now...do you like it?
Personally, I never go without gloves in the forest. Leather, vinyl coated (I like the Atlas...) and cut safe chainsaw gloves are always in my reach , most often on my hands.
Do you 'like' your left hand , do what you should.
Protect it.
( I do mostly forest restoration- as a 75 y/o volunteer, so I need to haul a lot of rough wood-gloves for that seem reasonable...all PPE for chainsaw is mandatory in my mind, you may disagree - that's OK ... but I cannot do this work with only one hand. Nor could i hug my wife in the same way I like too. You may have other priorities. So be it.)