It's hard to understate just how important the postal service was to the country: beyond driving so much commerce (and hence making mail deliveries a valuable target) it was used for all kinds of official documents and financial documents (money orders were introduced to reduce the risk further). Travel being expensive and hard, no alternatives like phone or email, etc. means that you send letters a LOT and things like postmarks or registered mail signatures have a substantial legal weight. Making a highly trusted service with special status to deter thieves available to everyone at a modest fee was a really smart move.
Not merely threats to the postal service itself, but threats via the postal service. I imagine the best to get away with (say) fraud has always been to avoid physical presence, i.e. using mail.
This is the territory where police departments and agencies get themselves into trouble - investigating crimes that aren't really their job to investigate. They technically have jurisdiction over a specific location or process, and that gives them an excuse.
The most obvious parallel is pretext stops - state cops, sometimes local, coming up with an excuse to pull someone over on a highway, in order to check them for warrants or in hopes of discovering contraband they have no reason to suspect exists.
A less obvious example is immigration enforcement fishing for excuses to deport someone.
I'm sure that the recent shooting of their FedEx colleagues in Indianapolis is on the USPS's mind as well, and I wouldn't be surprised if UPS and DHL tries to monitor social media as well.