A Constitutional Amendment was the end goal of their "great crusade" and they believed it would put the matter beyond repeal. Further, dope isn't alcohol, just as it isn't the right to keep and bear arms.
In truth, it was, at the time, regarded as necessary because most folks still understood (in 1919), that the powers granted to the Federal government under the Constitution were few and specifically defined, while the rights of individuals are many and not all listed in the document. Reread the D of I, and the IX and X amendments. In 1919, folks understood more clearly that if they wanted to grant more power to the Federal Government, it had to be done via Constitutional Amendment, a deliberately arduous process.
You are right that "dope" is neither alcohol nor RKBA, but the point is irrelevant and immaterial. The power presently assumed by the Feds to prohibit possession or use of "dope", is illegitimate on its face, regardless of whether one thinks that "dope" ought to be prohibited or not.