Let’s assume the money supply is fixed.

If productivity rises then yes, prices should fall, if we also assume demand remains constant.

If demand falls then prices might collapse and the additional productivity is worthless.

If demand rises as productivity rises then price might stay constant.

Assuming a fixed money supply, prices are a function of both demand and supply.

If the money supply is not fixed, then prices are a function of demand, supply and money.

In any monetary system demand is crucial in order to justify supply. If demand falls then there is no value to additional supply, whether that additional supply comes via productivity gains, cheaper resources or whatever.