>>adding qualifying criteria

It is not merely adding qualifying criteria, it is setting qualifications AND sortition to select legislators and executives.

>>solve a problem that hasn't been demonstrated to exist ...The main threat to a well-functioning society are people acting in bad faith.

Your second sentence there is entirely correct, and specifically disproves the first. We have a problem

>>we should test it at a smaller scale, such as a city for instance

100% agree, we should test and adjust any changes before scaling up

>>start without any criteria and see if that works well enough

We've pretty much demonstrated that it doesn't

>>uneducated people may not be very effective in coming up with solutions, but their presence is important to remind educated people of their existence.

We do not need to hand uneducated people the keys to power to be reminded of their existence, any more than we should give loaded handguns to toddlers to be reminded of their existence. Intelligent people suitable for leadership can remember the existence of both just fine, thank you. Moreover, with qualified sortition, the selection is random so it is highly likely that qualified, educated, accomplished people who are adjacent to people with issues will be p[ut in power and able to do something for them