There are indeed ways to design it poorly; I'll just point again to juries to say that we know how to do it competently. I'll rephrase the objections in terms of juries (but please note the quotes are from a hyperbolic strawman, and not literally what you said. I hope my replies to the strawman are still useful).

"People who don't care about the particular law/case will refuse to join a jury and they'll all get stuck in endless deliberation" - being on the jury is not always optional! While there are strategies to avoid being a juror, the large majority of folks don't use them. People get real nervous about perjury. Also, we have several levers of control here. Congress salaries+benefits aren't bad, getting an important position might be akin to winning a lottery. Many folks skip voting day because they feel uninformed or are required to work, but we educate jurists and require companies to give time off for their service. Finally, if a jury is stuck we call a new one; by random draw we'll eventually get a lot of all people from one side or the other. Gridlock is only ever stochastic.

"People could bribe the juries for the outcomes they want!" - extremely risky, the state knows who is on the jury at the same time as everyone else, predicting it ahead of time is impossible, and we strongly regulate the interactions of juries + invested parties once they're chosen. Note that we can assign political decision bodies to fairly narrow issues, so managing this at scale isn't so difficult.

Virtually every poll shows that around 1/4 to 1/3 of the population are Nazis, so it's only a matter of time before one of them gets picked

The laws are currently written by lawyers for bankers

Changing to a system where laws are written by actual humans instead of demonoid homunculi will alleviate a lot of the pain revolving around the apathy and complexity pain points.

Which, under a sortition vote, would mean we would have a chance!

The upvotes are in! There's at least dozens. 2 dozens.

I think we haven't tested democracy variations quite far enough. I agree that the first-past-the-post model in capitalism has proven extremely vulnerable to mis/disinformation, and made it possible to benefit from the idiocy of your peers. But I don't think we've seen, say, RCV and proportional representation + robust finance laws prove nearly so bad.

Also, I think this take is disingenuous to the roots of democracy. It is a social technology used for legitimacy in tons of situations by many groups, for a variety of reasons. Often it is neither dumb nor a method of obvious control.

You can do it several ways. Athens had anyone who wanted to from the city meet and interview the randomly chosen folks; if the group disliked them, they were removed from the pot and you drew again. Seems like a good fit when the job is comprehensible, and/or needs community backing. Similar in flavor to senate confirmation of appointees.

In juries, we have professionally licensed advocates and referee's who interview the randomly chosen, and they can reject folks for almost any reason they want. This seems like a good fit when we already have a big body of bureaucrats and managers who will need to work with these folks. Let them do the filtering.

For perpetually rolling positions, give the outgoing folks a small number of vetos on the next draw. They know what the job requires, and limiting the number of objections ensures against corruption.

There's also levers you can pull if we don't have a good way to judge competence. My favorites are to increase the number of people on the panel/jury/group, and provide larger budgets and opportunities for the group to get training. Just as congress (and courts) can pull in industry leaders, expert scientists, and decision makers, these decision making bodies should be able to do the same.