Minor thing about starting conversations on the street: some folks just don't want to be bothered in the middle of their own thoughts as they're walking. If you feel weird approaching random folks - that's just being an empathetic normal person. Nothing wrong with being embarrassed - because it is weird.

That said, I do agree that practicing facing rejection is a good exercise. I just feel better about that exercise when it's done as part of something useful to others - e.g. handing out lunch coupons, etc.