I wonder if it would be a good idea to render a standard email/usenet signature delimiter (that is, a line consisting of exactly two hyphens and then a single space; "-- \n") as a horizontal rule, or something similar?
Would this cause any problems?
Yes, of course. But the signature delimiter is two hyphens and then a space, not three hyphens. It has been around as a convention since the very old Usenet days and is still used and handled specially in a lot of mail and news clients.
See its mention on Wikipedia, which references three standards documents.
For whatever reason, as “standard” as this may be, it was not in the original 2004 version of Markdown … so it’s not included anywhere, and probably won’t be.
-- \n
An omission of this type would be odd since the people behind Markdown (Gruber and Swartz) would certainly have studied and known existing usenet conventions extensively.