pretty sure we can find something better for batteries than lithium

Trust me, bro

would you need someone scanning groceries if there was no money?

Because this is the most efficient way of keeping track of how many goods leave your moneyless store, and ensuring assholes aren’t just taking everything for themselves and hoarding it. Tracking how many goods leave the store at any given time allows you to order an appropriate amount to keep things in stock so that people who need things don’t go without, and is especially important for perishable goods like fresh produce.

What’s left can be rotated out or done by lottery,

People have different skill sets and specialties. Many jobs take years of training and practice to reach an acceptable level. Also, you just invented state-sanctioned slavery/a non-military draft. What do you do with someone who refuses to perform their lottery-assigned job?

and those doing the undesirable labor get to have more luxury items or whatever.

That’s literally the system we have now, but more authoritarian, since someone has to decide what is a “luxury good” and how much undesirable work is required to attain a given level of luxury.

people have been doing it for centuries.

Citation needed. Concerns: authoritarianism; scaling; maintenance of the modern standard of living