Chain saws with their steel teeth and often abusive cutting conditions
(especially if the teeth contact dirt) have to be sharpened way more
frequently than table saw blades. Notice how chain sharpening
equipment can be easily used sitting on a log in the woods? That's
where you are likely to use the equipment. I often take a break to
sharpen during extended cutting sessions.

I suspect that the bar paint is gone on account of contact with the
wood instead of heat. Your heat question does make me think though.
The 346XP takes a 3/8" pitch narrow kerf chain, right? Maybe the
narrow kerf chains aren't as tolerant of hard use. Otherwise why
wouldn't all saws come with them?

Your saw is probably fine. In the future change or sharpen the chain
sooner. Were you bucking thick logs non-stop or felling and limbing?
I think of the 346XP as a felling and limbing saw.