You might be doing yourself a disservice. There are a lot of people who would be extremely competent in practice who are put off by the dirt and competition of the election process.

Choosing officials by lot is also extremely resistant to the money-in-politics problem and corruption amongst officials (it becomes easier to detect, and occasionally you get incorruptible people in the role).

The ideal political system could well be random lot to determine a small pool of candidates (I think 3-4), then voters choose 1.