I believe you - thousands wouldn’t
I still think it’s cobblers. To cease something is to stop, to desist is also to stop.
I put that sort of language in the category of hoary old phrases passed down from the ancients. We have a lot of those ‘doublets’ - two words pretty much meaning the same thing which are nearly always both used when just one would do. For example “fit and proper”, “lands and tenements”, “will and testament”.
I’m more with this guy than with Wikipedia on this one.
See also here if Wikipedia is your preferred source, especially the section on legal style: