You are on the right track. Snail mail, letters, and correspondences were first class citizens in terms of things like protection by the Fourth Amendment. The postal service (at least as far as I am aware), is one of the few Third parties you can share that type of sensitive information with and have it by the letter of the law still be protected by an expectation of privacy.
(If there is a lawyer in the house who could let us know otherwise, that would be awesome).
The Supreme Court, however, has been reticent to apply any interpretive oomph to the idea that electronic message sending represents the same type of "private correspondence" that a snail mail letter represents.
In fact, if anything it has generally leaned in the opposite direction. The SC has ruled that sharing personal or private information with a third party thereby nullifies your expectation of privacy and protection of your information by due process. This happened in the early days of telephony I think.
"But that is only from the Government's point of view!", I hear from the gallery...
Yes... Unfortunately it does set a societal precedent through the institution, however.
I mean, if as an arbitrary business, I can hand your information to the government and they can make use of it, then surely I am free to share data I have about you with other people\businesses?
Once that becomes legally acceptable, and people are willing to pay me for as much info as I can give, suddenly the economic incentive is to collect and sell as much information as possible. Note that this isn't a tech problem, but a social one.
As long as we don't take a stand by making law to cover the issues of electronic activity being considered "protected correspondence" with a reasonable expectation of privacy, we will continue to see these blatant invasions into our personal affairs by business and government alike.
The thing that will hold back that lawmaking though is that there are some VERY deep pockets that would see incredibly vast revenue streams dry up by passing something like that.
One could see places like Alphabet, Microsoft, Facebook, and the other Silicon Valley darlings doing everything in their power to convince both the government and the populace that doing something like that would be a terrible idea.
And they would be right to a degree. Many "free" services would have to switch to to a subscription model or something similar, and it could mean major cutbacks for many tech companies that haven't matured enough to diversify away from an ad supported business model.
I can't speak for anyone else, but to me, that is a small price to pay to establish a right to the privacy of the exercise of our wills in the electronic realm. Thinking in the Internet age is truly an inspiring thing to behold. However, the Net that enables this capacity for collective thought is just a tool. We will get out of the Net what we as people put into it. To me, the Net has always been about empowering and uplifting every person by putting the collective knowledge and wisdom of humanity at each person's fingertips before anything else. One should always come away from the Net having found something, but at the same time, one has the right to use the Net and not have anything TAKEN. A "Right to Lurk" as it were.
If I had to choose something as the basis for a new Constitutional Amendment, it would be something that would explicitly codify the expansion of the legal "expectation of privacy" to encompass all electronic forms of communication, commerce, and assembly; protecting the aforementioned from search and seizure by the government without due process. It wouldn't do anything for SciHub sadly, but it would be a step back in the right direction in terms of curbing some of the more demonstrably harmful ills the Net has facilitated in our society.
P.S. Sorry for the mind dump. It felt great. If you are still reading, you're awesome.