If Clinton can run her own email server, why are so many people allergic to running their own servers? (PS, hope she had a business internet connection so she wasn't violating ToS)
1) they are accountable to the people. Granted this is a principle. At some point in the future, everything the federal government did will become open knowledge.
2) It must be possible to get them in front of the justice system. This is a basic principle of a separation-of-powers democracy. The justice system is, by law, entitled to access any and all documents, emails, everything any agency has (just so we're clear : not talking about the judge down the street, although they have some access, but the supreme court has full, unquestionable, access)
3) FOIA (freedom of information act). Citizens and others can petition the justice system to make government documents public. Unless the justice system and the federal government agree something can not be made public, it is made public.
This is extremely prominently mentioned on every computer system anywhere near the federal government. Record keeping requirements this, email archival that.
Ms. Hillary Clinton did not miss these requirements. She knowingly violated the law and conducted official government business in an illegal manner. Ms. Clinton knowingly, and with the aid of dozens of people working for her on the public's dime violated the law. In theory the minimum punishment for this is to become unelectable for 5 years, but "somehow" I doubt that will happen. Also there seems little doubt that the emails she will make public will be a filtered version of the original.
This is comparable to fraud (though technically not fraud) : if you did this as a CEO of a publicly traded company, it would be considered fraud, and you could very well go to jail for that.
However, I do think it would be cool if people had a turn-key solution to host their own email solutions on a cloud provider or something. :)
You also need to take steps to ensure that your email will get to where it is going. That means configuring authentication protocols like SPF, and taking steps like using a fresh IP address for your mail server, and warming it up so remote ISPs begin to trust it. For most email providers, the default status of new sending IPs is "suspect." You can't just stand up an email server and expect your emails to hit everyone's inbox.
This does not even get into the security aspects that apply to running any server on the Internet.
Legal protections are one of the only reasons to bother that I can think of. When your email is hosted by Google, Google can provide it to legal authorities without telling you. When it lives in your home or business, you will know if someone is asking for it.
We moved servers to a new block of IP addresses, and after a couple hours we found ourselves on Microsoft's spam list. Took about 20 phone calls and almost 48 hours to get off of that thing. The other big lists didn't make a peep.
Secondly, I think your last sentence answers the question. Running one's own email server isn't "normal" these days; email-as-a-service is such an over-solved problem for the average (security-unconscious) user, that going to the hassle and risk of running one's own is generally the purview of people who have something to prove, something to protect, or something to hide.