That's a great workaround, dwaflord. Thanks for the idea!
I'm not sure if this was added in a recent version of Acrobat Pro, but there is an "Add Initials" option in the "Sign" tool now, and I was able to type and place a date into that.
For all of you quibbling about metadata: Please understand that not every signed document's end-us is to be saved as a digital file. Often, even in 2018, we are submitting to companies that are printing and filing the paper version of a signed file, and in those cases, a visible, printable date is necessary and the metadata is a great "progressive enhancement" useless in a practical sense.