In true HN fashion, I suppose I must be FULLY explicit.
“What’s the rationale for legalized sports betting [that mirrors the rationales for these other two decisions that you are placing in the same category]?”
“Just make money” or “the Romans did it” are unlikely to fit the bill.
Why do people invest? To make money.
Sounds more like you're wanting to ask a more generic question on why addict gambles, but if you want to understand the rational of an addict, then get in line. The only thing to understand is trying chase the high in whatever form it takes. Ask an addict and they will tell you there's no explaining it.
To me, the "HN fasion" is not accepting that there are things that exist that are not rational and no matter how much you want to logic your way to an answer, it will never happen.