No they won't. You're missing the other half; if labor becomes free, the fruits of that labor become exceedingly cheap or even free.

See: the rapid drop in cost of food, manufactured goods, etc as automation took over those sectors. No one starved when we automated farming; they got fat.

Destroying planet in the process.. NOTHING is fucking free.. wake up.. It have costs. Energy and waste (waste needs to be reproceesed so energy again).

If you take a look how much energy is put into producing 1kcal of food, you will see that its negative. We put around x6 more that we get (diesel, syntetic fertlizers, water pumping, etc). This is because we have cheap energy, like fossil fuels.. Unfortunatelly, it have hidden costs smartasses didnt anticipate.