I will respectfully disagree on this one Sir.
What about Gillette slide (aka guillotine slide) motion...?
It is exactly going sideways, while going down simultaneously. Today we have slant head DE razors to mimic this.
Obviously you need to be careful and not go sideways too much, but it's a great motion IMHO. It really helps in getting a close shave.
Some people do this even with traditional SRs, let alone DEs.
You are absolutely right, of course. However,....this move is NOT for a beginner, and the key is (as I'm sure you know) in maintaining the CORRECT (and continuous!) downward motion as one goes sideways. IF one stops going down (while moving sideways), the nick (or long cut) is the result. This is what I tried to explain in my post, but since English is not my first (not even second) language, I sometimes omit the important part of description.