Sortition is the term you're looking for: https://en.wikipedia.org/wiki/Sortition

Western democracies would be far better off with some sort of legislative body that was comparable in power to the existing bodies such as the senate / parliament.

Another solution to our existing problems in western democracies would be a mechanism to select 'none of the above' on a ballot. If a super majority of the electorate chooses the 'none of the above' option than that election is a do-over and the candidates who ran are forbidden from running in that jurisdiction for a period of time -- let's say five years.

A couple cycles of that will flush the crap out of our system real quick.

But like you said... the system is run by lawyers, for lawyers, so we're not likely to get these kinds of changes.