Unless it's chainsaw racing, where it's all over in seconds, it's pointless getting the cutters razor sharp. Unlike other wood working tools there's very little cutting by chainsaw chain, it's basically a "puncture and tear action". To assist maintaining this action, cutters are made by using a "softish" steel", that can be easily removed by filing , and the main wear surface is plated with a chrome hard plate. All filing does is remove the underlying steel to expose a new section of Cr plate which breaks off leaving a new hard edge. That edge is not razor sharp, in fact its pretty ragged compared to a fine wood working blade, a bit like a serrated bread knife. Due to its large grain size it is also quite difficult to make the Cr plate razor sharp.
The main job the Cr edge is not to cut but to survive high impact while being driven repeatedly into wood. If a chain is made razor sharp by honing (I know someone who does this to cut firewood
) the very fine edge is lost in the first few seconds of the cut. Provided any glint (a sign that remnants of the old rounded over Cr edged is still present) is removed along the edges of cutters that's all that is worth bothering with for CS milling.