You want your oil (and grease) in the bearing surfaces, not in nooks and crannies. Tackiness can indeed be good though.

Oxidized vegetable oil is the most disgustingly tacky substance that I know. It's like a cross between rubber, glue, and grease. It is very resistant to removal with "intuitive" methods (but using un-oxidized oil and heat tends to work) and it doesn't lubricate, it sticks. It can't possibly be good for lubrication, I'd say. Unless you can somehow control the process so that it oxidizes just a little.

Well a slimy sticky surface rubbing against another slimy sticky surface doesn't cause wear.

And in a chainsaw, it's mostly wear you want to reduce. The frictional losses in the chain are low compared to the massive friction in the blades.

That's not how vegetable oils gum, they go sticky in a way that's not like grease. Hard to explain but if you feel them both there's a huge difference. Grease will stick but isn't stick-y in the same way if that makes sense.