Random selection is necessary to create stable meritocratic institutions

The underlying assumption here seems to be that there is no or even negative value in someone actively specializing their labor into politics, and I just don't think that's true. To the extent we have to "do politics" at all [1], it's probably best handled by the people who have dedicated their lives to becoming politicians, the same way that getting your house wired is probably best done by someone who spent their life becoming an electrician.

In fact, if anything, this system seems like it would be even easier to game compared to the status quo. If you select truly at random from the population you're going to pull a lot of people with not a lot in the way of resources, making for a very easy to bribe block, even if you have to repeat the bribes every few years as people shuffle through. If you don't - if you select randomly from, say, only the group of people who got perfect scores on the SATs, or from white land owning males - you're practically begging for tacit collusion as they realize they have essentially the same power that HOAs do when it comes to what we'll do next. Democratically elected politicians at least have enough sense to understand they have to balance their short run desires with their long run interests in continuing to be democratically elected politicians.

[1]: Which I don't admit we should in the first place, cf https://spot.colorado.edu/~huemer/papers/passivity.htm for one reason why.