Hey,
It's not stupid at all if you are into it, but crashes on the street result in impact injuries from hitting stuff like cars and poles, the type of stuff that breaks bones.
IMO moto cross gear is best suited for street riding and it's hazards because it distributes impact much better than road racing leathers.
Any armored jacket, jeans, good gloves and shoes that cover your ankles are adequate for the street.
At the very least gloves, denim jacket and jeans. Anything less than that and you are just plain stupid.
Street wear should have a different type of protection IMO, Impact protection.
Leather was pretty hot today, got to get a mesh soooon!
Ooops this has been mentioned, I'll leave it here anyway.