As a cyclist, I sometimes see cars approaching crosswalks at a crawl, just creeping along at a few feet per second. I do that on my bike too, because I'm hoping the light will change before I have to come to a complete stop and put my foot down, but I have no idea why drivers do it, and it definitely doesn't feel safe crossing in front of a car like that.
In an automatic car, it's just about fuel efficiency and wear/tear. In a manual, it's that plus it's extremely annoying to stop and go at each semaphore.
Coming to a stop and just sitting there can warp the brake rotors. The area under the calipers doesn't cool off as fast as the rest of the brake rotor, and the localized heating causes the metal to bend.
You're supposed to creep forward a little, but some people might be overdoing it.
