There's also a benefit in visibility. Even if you fix everything else constant (same number of cars, at the same distance, etc.), it's safer to cross the street

There's also a benefit in visibility. Even if you fix everything else constant (same number of cars, at the same distance, etc.), it's safer to cross the street when someone else is already crossing than it is when no one else is crossing. It makes sense that someone being willing to cross at a red could push others over into deciding to cross.