I mainly use regular sewing machine oil, though I have also used Tri-Flow on occasion, though I don't buy the really gnarly, seized machines. The ones I buy move freely.
Whatever additives are in ATF likely won't stick around on a sewing machine, but for freeing up stuck machines, it may work pretty good.
Lack of regular oiling, and prolonged periods of disuse are probably what cause varnishing and stickiness, and not using plain old sewing machine oil.