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If you've already built the infrastructure and practices to smuggle an illegal good, it is unlikely that you immediately start paying taxes once it becomes legal.

The illegal sale of something has risks and costs (obviously) so the criminals will only engage in it if the price of the good being sold is high enough. When prohibition started the price of alcohol went up to cover the risk of selling it illegally. Once prohibition ended the price dropped and it was no longer worth the risk to selling it illegally.

However, you are correct that they had already built up the infrastructure and practices for smuggling, so they simply moved to other more profitable goods like guns, harder drugs, and people.

Or that the illegal trade carried on for a while after, thus reducing legal sales.

Assuming the black-market networks created as a response to prohibition shut down completely, of course. They may have continued operating as a means of tax avoidance, leading to less taxed consumption post-prohibition.