you’d still probably pay less for a meal

But your cost of living for everything else goes up.

what’s wrong if some of the wealth gets distributed among the other hardworking staff in the supply chain rather than be concentrated in the hands of the last step of the chain and

Raising the price floor for wages doesn't guarantee anything, the various industries in the supply chain could just cut employees and make people work harder or take steps to automate production.

it raises the floor for the kind of standards that restaurants can have for the most vulnerable worker

Or restaurants just switch to kiosks, we dont need servers to have a functioning restaurant.

Minimum wage increases cannot solve poverty, only redistributing the means of production to the working / poverty class can do it.