I think the reason to teach something like changing a doorknob isn't really because they're going to need that specific skill. I'd consider teaching it because it's an easy demonstration that taking things apart to fix or change them isn't necessarily a scary thing to do. I bet a lot of people with some minor problem to fix in their home wouldn't be able to do it, not because they can't use a screwdriver but because their instinct is that they are supposed to get an expert to do it.

You can very easily teach how to change a tire at school. Assuming the school has a parking lot, you just walk out there where you have literally any car parked. Then you change the tire. Even in an urban setting, this is quite easy by simply walking to the nearest location where you can park a car, and practicing on a car that the teacher has parked there earlier in the day. Changing a tire is an extremely simple skill that could be taught in a single class period, but many motorists lack it and end up stranded on the side of the road because of their lack of knowledge. If they break down in a convenient location, this may simply cost them time and money as they wait for someone to come along and do this task for them. But if they are in an isolated location - say, on a remote road in the mountains during a blizzard - this knowledge could save their lives.

why bother when cars don’t come with spares anymore

how many flats do you get?

Are stupid? You get CPR trained not because you expect someone to need CPR every day, but because you want to be prepared in case you ever need to do CPR. If your car doesn't come with a spare, go buy a spare. Don't get fucked over just because auto manufacturers are cheap bastards.

Changing the oil varies hugely per model too.

Why would you need to learn how to change a doorknob when that varies quite a bit per model?

This is not true, like... at all. There are some minor differences with, say bolt sizes, oil filter types, existance of retainer clips, etc. But the process of changing the oil in a passenger vehicle is pretty universal. Same with doorknobs. I'm sure there are some weirder varieties - but every doorknob I've replaced follows exactly the same process. Slide the bolt in, put the knob turny-boi in the bolt, finagle the machine screws into position to connect inner and outer knobs, tighten machine screws and the screws that hold the bolt plate into the door.

None of this is rocket science, but as the other poster said, most people's issue is simply the first step of believing that they can successfully complete a repair or maintenance task themselves. There is nothing special about replacing a doorknob, but it is a simple and useful demonstration assignment that can get kids comfortable with actually using tools and taking things apart, and that is an extremely useful life skill.