It's not a common request here. Whether we'd comply depends on the call, location, and time of day. We usually approach lights-only once we're in a quieter neighborhood anyways, especially at night.
As for why it would be requested... privacy can be one. In some areas, a lot of bystanders will congregate to watch what's going on. I remember another crew on my shift getting that request for a family where a teenager was having a miscarriage. I can see why they'd want to avoid having nosy neighbors ask about that one, although I can't really see why they wouldn't just make something else up. As I recall, the crew did approach without l/s. Sometimes sirens will also scare small kids, so I could see parents wanting to avoid that.
Edit: I forgot about being requested to stage off-scene by law enforcement. In that case, you can bet we're going to turn off the l/s as we get close, even though we'll be staging somewhere safe.