The Code of Federal Regulations section governing mail covers seems to indicate that the requirements for requesting a mail cover create absolutely no protections for USPS customers. For purposes relevant to the article, section 233.3(e)(2) is the most interesting. All that is necessary is to "specify the reasonable grounds" that national security is endangered, a fugitive is involved, a felony might be involved, or that forfeitable property (probably cash and/or drugs) needs to be identified. The request need not be restricted by person or place. If I think Walter White is cooking meth, the DEA can literally ask for a cover of all mail that passes through the USPS system, and the Chief Postal Inspector (or either of 2 possible designees) could give it to them for 30 days. Only communications KNOWN to be between a subject and his attorney are exempted.
Sections CFR 233.3(f)(2) and ASM 274.5 imply that the USPS cannot record data from the outside of mail in the absence of a mail cover order or other prescribed reason. That, in turn, implies that since (according to media reports) they have been doing it continuously since at least 2001, the head of DHS could simply be requesting a mail cover monthly, to support investigation of unspecified threats to national security. The CPI is required to keep those mail cover records for 8 years, though the data the send pursuant to those mail covers would be governed by the receiving agency's rules.
I would argue that the protections the USPS already has in place for the prevention of mail tampering generates a reasonable expectation of privacy in the external appearance of mail entrusted to the USPS. Since the mail must be placed in approved, closed, and statutorily-protected receptacles, are protected from viewing and tampering in transit, and delivered to [potentially lockable] receptacles, the mail itself is never in public view. There is no vantage point from which an ordinary member of the public could see and record the external mail data included in a mail cover. When I write a letter and mail it, I don't expect my neighbors to know to whom it was sent.
The courts have determined otherwise. In theory, the only way to trigger reconsideration would be to follow around postal delivery trucks, photographing and replacing mailbox contents. When you get arrested, bring up the precedent in your defense.
Mail exteriors are either private and confidential, and thus worthy of "reasonable search" protections, or they are not, and anyone should be able to photograph your mail. You can't have it both ways.