All true. I can only assume that slamming the throttles to idle in a similar situation would make it even worse.
Not a typical wind to be sure, but have seen it come pretty close more than once descending out of a jet core landing in the tropical Pacific. Shear layer about 5-10,000 feet thick, well below the high tropopause typical of the latitude. Hence "chasing the Mach" in the descent. Seen the "open descent Mach dive" more than once, usually with inexperienced crews. They usually catch it right away.
A managed descent in managed speed, with a good wind profile inserted, makes the whole thing a total non-issue.