Actually it's necessary that enough, if not most, things do, else the lost jobs will be lost forever.

But you're worse mistaken than just in quantity: there's no mechanism to make things that can't be automated more expensive. If anything it's exactly the opposite: they'll become cheaper and more plentiful:

a) automation removes N jobs

b) people who previously did those jobs turn to whatever they can find -- and they mainly turn to do what can't be automated.

c) we now have MORE people doing what can't be automated: the people that were already doing it before automation, and the people who lost their jobs and turned to "doing things that can't be automated".

d) Abundance of workers making those things (or offering those services), drives labour costs down, fills the market with those things/services and makes things/services that can't be automated get more devalued.

I understand it perfectly well it's just wrong.

I didn't ask you to be right all the time, you set that bar up yourself by claiming that things that couldn't get automated would get more rare.

I just gave you an example of something that wouldn't get more expensive even if AI couldn't do it. And now that I think of it I am struggling to find anything that will get more more scarce if AI do almost everything else. That just means more humans, more potential competition and thus less rare.

Perhaps DanielBMarkham is an advocate for Basic Income?

Because in a world where we've automated away most of the good jobs and the threat of no job means being destitute and on the street, your argument that house cleaners become abundant seems irrefutable.

In a world where I balance my dislike for cleaning toilets with my desire for a slightly larger share of the robot-generated bounty, it's not clear there would be an over supply of house cleaners.

I am pretty sure there would be as Basic Income + Income makes you richer than everyone else who only live of Basic Income.