> Am I to understand that official orders that instruct telco providers to provide the private communication data of people, are transmitted as smushes of pigment on thin pieces of wood-paste,

Yes. Or a PDF attachment on an e-mail, possibly scanned from something that was printed a few minutes earlier because someone had to sign it with a pen.

> trivially verify with the ordering entities public key

You're underestimating the complexity of establishing a PKI infrastructure to handle federal, state and local authorities, signalling which keys have what exact authority, revoking compromised keys, … and then doing tech support for some redneck judge that owns more guns than electronic devices.