The 21st Amendment (which repealed prohibition) explicitly grants states the right to regulate alcohol imports and possession.
[The Congress shall have Power] To
regulate Commerce with foreign Nations,
and among the several States, and with
the Indian Tribes;
But yes, the reason the regulation is different for alcohol than for other goods is ostensibly the 21st.
I.e. it's just the academic point that it's not inevitable that the Federal government uses the power of the CC to enforce free trade between states, that's just how it's chosen to implement it.
I.e. there could be an alternate timeline of the US where the CC enforces the ability of individual states to impose interstate tariffs up to some threshold, similar to how the EU manages agriculture quotas within the single market.
I.e. the CC isn't some clause saying that free trade between states must be respected at all cost (sans the 21nd). Otherwise why would there be a federal drug law on the basis of the CC? That's a prohibition of the sale of certain goods on the back of prohibiting sales across state lines on the back of the CC.
Hence the indirect reply to SeanLuke upthread. This is not a violation of the CC, but of some federal statute enacted on the basis of the CC.
The distinction matters because if the CC isn't an amendment that ensures free trade the federal government could just as well use it to ensure trade restrictions between states as free trade, which it mostly does today.
The interstate commerce clause gives Congress the power to regulate (make normal) commerce between the states, removing the power of states to impose tarrifs or other barriers to trade. This was a big problem at the time. The 21st amendment specifically makes an exception to this general clause in the case of intoxicating spirits.
Otherwise, yeah, the Articles of Confederation weren't working.
From Wikipedia: "The context of the 21st Amendment, they wrote, was to return to the status quo that existed before Prohibition, making it clear that the states had the power to regulate alcohol however they wished, including banning alcoholic beverages entirely within the state if desired. Before Prohibition, the states did not have the power to violate the Dormant Commerce Clause, and the 21st Amendment was not intended to grant them this power."