> I wonder why states/municipalities don't just leave it at that - a specific consumption basket whose cost is recalculated annually, vs having recurrent loud debates about it with some arbitrary round numbers.

Because the level at which it is safe to set local minimum wage without net adverse effects from job loss depends on a variety of conditions besides price levels, including prevailing low-end wages in localities that compete to attract employment. Building a formula that fully addresses this is nontrivial, and even with one that worked locally there would be a reason for broader regional/national campaigns to kick the floor up.