Keep in mind that the USPS can (and does) scan the front and back of envelopes[0]. Keeping this information indefinitely is tantamount to storing email "metadata" (information which is intrusive enough that it's what caused Groklaw to shut down).
Also, it's easier than one might think for a determined adversary to discern the contents of the letter - either by opening it carefully so that it appears unopened, or by (e.g.) shining a light to
There are defenses against this too, but I wouldn't assume the physical post is inherently more secure than email.
[0] http://www.nytimes.com/2013/05/04/us/where-mail-with-illegib... - I can't find the original link that asserted that they store this information indefinitely, but IIRC the USPS didn't make much of an effort to hide it.