I can't imagine a planer without depth adjustment. Every sidewall is different and planers don't want to hit metal, just plastic.
This is what a round cutter does. The sidewall is very much out of the way, too much for what I would consider doing today.
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This was done for me a long time ago. While I have no complaints about how the ski runs, I prefer using a file to simply remove a little more sidewall each time, or when necessary. I don't file my skis very often, but when I do, I like to leave as much sidewall to support the edge as possible. Using a Panzer and higher bevel works for me.
As
@Jacques points out, you only should plane when filing. I interpret that to mean, if you are just stoning your edges (and did the planing right) you don't need to for stone touch-ups.
Jacques, I would think you could use a square/straight knife on sandwich skis.
You also said "If you get a chatter, it is usually from a hard spot. Further soften with paper or a 100 grit stone, then continue. " Another reason for chatter is taking off too much at once.
In closing, on my skis, I think too much sidewall was removed, possibly weakening the support of the edge. We can't put sidewall back if we take off too much. Likewise, we can't undo bad chatter of the blade. Practice, practice, practice on skis that don't matter to you and know that every sidewall is different. Different shape, different material. They all cut differently.