Clearly they had several skinfuls at the Cana wedding, and at the Last Supper too, but those were special occasions. Was it an everyday drink for your ordinary Joe? Or a luxury good? It makes a big difference to the significance of the Eucharist. If wine is the drinking equivalent of bread - the most staple of staples - then that gives it one kind of significance. But if it's seen as something special, that gives it another.
Even if wine flowed freely and cheaply in Jesus's particular time and place, that certainly hasn't always been the case in the cultures to which Christianity has been introduced. It must have been another story in beer-drinking countries such as Egypt and Germany, for example. The same goes for England, where wine was seen as a posh drink until very recent times. Telling an Anglo-Saxon peasant to drink wine in memory of Christ must have conveyed a very different message from telling a first-century Roman to do the same.
Christopher Marlowe is said to have joked that the Eucharist "would have bin much better being administred in a Tobacco pipe" - and after all, why not? One for the alternative historians, perhaps.