Yeah, but even if they're arrested and the charges are dropped, they still have an arrest on their record, which many/most colleges ask about on their applications.

Watch the John Oliver episode about School Resource Officers, you'll see one girl arrested and charged (I believe they dropped it though) with a felony/bomb charge for popping her water bottle cap like we used to do in school (y'know, twist the bottle, and then unscrew the cap and it pops off).

Another kid, special needs, was arrested and manhandled because he lightly carved "[Name] was here" into a concrete wall, which his mother had him come back and clean off. John put the kids name on his wall so that everyone would know "a legend was here," which is the reason the kid gave for why he did it in the first place.

Schools don't need cops, they need social workers, counselors, and proper funding. Not a chode with a gun and an authority fetish. Our school officer used to make friends with all the kids dealing drugs/getting in fights, while our principals/vice principals would scream at kids to take their hoodies off. And they wonder why kids think school is a joke.

But can’t most cops use their discretion and not arrest the kid in the first place bypassing the prosecutor completely?

That's just wrong... cops charge people and the District attorney will decide if they want to prosecute those charges and spoiler alert they do it 99.9% of the time.