But what’s the benefit? All it does is give “your side” some chuckles and causes “their side” to become defensive and attack you for something equally irrelevant.

You’re neglecting the third “side”. Those who are neutral. Criticising an opponent—so long as those criticisms are well-grounded and don’t cause a neutral observer to say “wtf are you on about, you’re obviously making stuff up”—weakens their ability to convert others to their cause.

you’re implying that anyone who is considering voting for them is “weird.”

Someone voting for them isn’t collateral damage. They’re the intended targets.