There are, according to standard capitalist economics textbooks, three key functions of the price mechanism: informing, incentivising, and rationing.
So, prices firstly collect and make available information about costs and utilities, secondly they ensure that producers have an incentive to make the right amount, and thirdly they ensure that scarce resources go only to those with sufficient desire/ability to buy them.
What might a communist say about this?
EDIT: In the interests of clarity – my goal in this post is twofold. Firstly, it is a critique of society as it now exists. This society is capitalist (dominated by a class who control the means of production), market-based, but not free-market based in the fullest sense (that dominant class has both economic and also political power, which it wields extensively, often distorting markets). Other societies, such as the USSR, might be called (loosely) non-market capitalist: markets were not central to the economy, but a class of capital-controllers were in power.
Secondly, it is a contribution to debates within the libertarian left. Some anarchist socialists support a large role for markets and pricing. Others, such as myself, are communists in the sense of generally supporting conscious collective planning over market-based coordination. In critiquing the claimed advantages of the price mechanism I am thus offering a comradely argument from one anticapitalist strand to another.
Not every point here will apply equally to both of these goals.