Sortition (the formal term for this) is very attractive, because it seems it would eliminate corruption and other political ills. The problem is that the bureaucracy (he part of the executive branch that has some legislative power) would grow, become more corrupt itself, and become very effective at manipulating the citizen-legislators. I don't think you can eliminate the Federal or State bureaucracies without also parallelizing the legislative process.

Now, don't get me wrong, sortition may improve things for a time. But like code, people figure out how to take advantage of laws. Re-writing the US Constitution on a regular basis is very risky; instead, SCOTUS changes it's opinion on what the Constitution means periodically; it's like updating the interpreter's code instead of changing user-submitted code.

You might also be interested in the districting method in which you draw district boundaries through the middle of high-population areas. Half the population would be on either side of each boundary. You keep subdividing until you have as many districts as needed. (Sorry, I don't remember the name for this, but it was the best option I could find when I last looked into this topic more than a decade ago.)