I was going to segue into thermodynamics as a backup example, but you made me think of something better.
> IMO a better example would be the stochastic nature of quality control in manufacturing.
How about, more specifically, food manufacturing? Or maybe, let's talk about cooking?
Cooking is as stochastic as it gets, and we handle it fine. It could be better - the better version is called "chemical process engineering", it's what cooking looks like when you care about quality and consistency of output, and can afford the equipment and process actually necessary for it. Regular people don't (i.e. neither care, nor can afford) - we call this cooking. It's an art, not a science, and people not only do it, but love it, and tie their identities to it, and build businesses around it, and a culture that embraces all the compromises (and calls the more serious approach "unhealthy").
My attempts at making bread have been too stochastic, in that it hardly ever produces nice results.
But yes. Eyeballing how much dried herbs to put in my dishes because I like what 2-isopropyl-5-methylphenol does for them. Usually it works, sometimes it's just a bit too Italian.
... in some sense, it's a miracle most people deal with this kind of bullshit without complaining much.
(Probably because they don't realize it's something to complain about. It's just how things are.)