Sortition is still an interesting idea. Especially for filling up larger decision making groups like a parliament. So that the law of large numbers can work.

It wouldn't be that useful for selecting a single post like president.

As a slight modification of straight up sortition, I would suggest that instead of picking the members of parliament directly, we still have everyone vote for their preferred candidate, and use sortition to pick out as many votes as we have seats to fill. (With some sensible mechanism for when the same candidate comes up more than once in the votes.)

That procedure would sidestep many of the problems that come up thanks to Arrow's Theorem in more conventional procedures or citizen's commissions etc.