Whether or not it was worth the cost is a separate issue; I think it's pretty clear that it wasn't. But the argument can be made that it did "work" in reducing alcohol consumption.
As for Jim Crow 'working,' it's notable that drug prohibition has 'worked' as a Jim Crow as well.
That aside, the parallels regarding stronger formulations and compounds is spot on.
It's just not the way "worked" is used, and falling back on the most literal, narrow meaning of the term actually signals conceding the argument.
"We find that alcohol consumption fell sharply at the beginning of Prohibition, to approximately 30 percent of its pre-Prohibition level. During the next several years, however, alcohol consumption increased sharply to about 60-70 percent of its pre-Prohibition level."
If I was trying to prohibit something but could only manage to prevent 30-40 percent of it compared to when it was legal I would certainly feel I had failed. This is without factoring in all the other problems Prohibition caused.