It's not obvious, but I think it does follow from the concept of general election.

The problem is that being informed and rational about selecting a suitable candidate is considerably harder than we think it is:

1. Society faces a large number of extremely complex issues. Candidate X says, "we should get rid of regulation Y." Are they right? Are they wrong? To figure that out, you need to know enough about the economy, about why Y exists in the first place, how many experts agree and why, how many experts disagree and why, etc. Just for this one issue, it will take hours. If you want to make an informed choice between two competent candidates, there's no way it will take you less than a week of intensive, full time study. At this point, you should damn well be getting paid for the effort.

2. How do you evaluate the character of a candidate you've never met? What if you don't know anyone who's met them? When you hire someone, it's best if you can meet them, talk to previous employers, run background checks. How can millions of people do this for presidential candidates, each to their own satisfaction? They can't.

3. How do you negotiate with fellow voters? If I want some things and you want some things, and we both need to agree on a candidate, the candidate I would pick in my corner and the candidate you would pick in your corner may very well be different from the candidate we would agree to pick if we could negotiate directly. If Clinton and Trump voters had been able to directly negotiate with each other, is there not a possibility they would have picked neither?

4. How do you get all relevant information? Depending on what is in a candidate's tax returns or on secret recordings, a voter may decide differently. Therefore, it makes sense that the voter would be able to subpoena some of that information, including classified information. After all, if I'm picking someone to run my country, I sure would like to see any classified information that betrays poor judgment on their part. In fact, I dare say that I need this information to do my job. But obviously it is still sensitive, so it cannot be provided to millions of voters.

I don't think general elections, where everyone votes, is a good system. It's not because people are dumb. It's because it scales poorly.

A simple alternative would be to pick a random subset of the electorate (a hundred or so) to act as voters, fly them to a convention center for a week, all expenses paid plus a sizeable wage, and let them interview candidates directly, subpoena relevant classified information, and negotiate with each other. I don't think anything short of that would work. Plus, it'd be much less expensive overall.