The most important assumption that supporters of Prohibition made was that outlawing alcohol would drastically reduce (and practically eradicate) its consumption. All their other assumptions flowed from this one.
The whole point of Prohibition was to ease the social ills that reformers felt were caused by the consumption of alcohol. Supporters thought that there would be less poverty and domestic violence. They felt that there would be increased worker safety and productivity. In short, they expected a better society to arise.
This was all based on the assumption that Prohibition would cause people to stop drinking. Of course, this assumption proved to be false, at least given the specific laws (actual consumption was not illegal) and the level of enforcement of those laws.