Alcohol taxes were huge. In 1900, they accounted for something like 30 to 40% of federal tax revenue.
Therefore, before you could have prohibition, first you had to have a replacement for the alcohol tax.
And that replacement was the income tax.
The prohibitionists were fully aware of this, and they were one of the main forces (maybe the main force) behind the income tax Constitutional amendment.
They used head taxes. If they didn’t have the revenue they required, they would tell each state, “Here’s your share. Raise it however you choose and send it to us.”