> Lack of children is about to bite us very, very hard.

Could it have an effect like the Black Plague, where labor becomes more expensive?

All things being equal, probably yes.

But remember: the uber-rich are allowing millions to immigrate to the rich world, to prevent precisely this. (I'm not commenting here on whether immigration is a Good Thing or a Bad Thing, simply noting that large-scale immigration brings wages down, and that the low birthrate is consistently stated as its main driver.) Also, remember that paying for all those unproductive old people will consume enormous amounts of wealth, something that didn't apply during the Black Death.