Undoubtedly, someone will reply to your comment with the quote from Nixon's advisor about how they invented the war on drugs to target the antiwar left and black people.
What happens is usually a mix of factors. Drugs aren't purely harmless, you can certainly find a few people who've been harmed directly and a larger group of people whose use is problematic. This creates a demand for Something To Be done.
This falls down on comparisons with alcohol and tobacco - both of which are widely legal and have their own temperance movements, but haven't quite succeeded in a total ban yet. America (and a few other places) actually did have a War On Booze, they just gave up because it's too socially normalised. Only the more extreme Islamic countries manage official temperance, and even there it's widely violated.
Drugs are an old thing the Opium Wars started in 1839 and alcohol significantly predates writing.
They might've given up because alcohol prohibition increased the crime and alcohol poisoning rates; because it was killing more people than it was saving.
They might've given up because the state prohibition laws had exceptions for religious and medical purposes and so were explicitly unequal ("de jure discriminatory")
Lots of people have argued that the same is true of the drug war, it's just that the mainstream discourse isn't interested in examining this as a factual proposition.
> They might've given up because the state prohibition laws had exceptions for religious and medical purposes and so were explicitly unequal
Same is true of the drug laws (e.g. opiates)?
Strict Scrutiny requires a law which violates equality to be the absolute minimum necessary policy which achieves the public interest objective(s).
But I don't think it's the only reason that recreational drugs were banned and have been kept banned. My other theory on why prohibition is popular is due to conservative Protestants believing that mind altering substances are immoral. I've encountered a lot of people who are against recreational drugs for the very fact that they are recreational (while hypocritically still enjoying alcohol).