"And headlights would work at the speed of light.."
Hmm, methinks you need to read up on physics a little bit.
Or think about this. If you could* travel at the speed of light and you turned them on, are you saying the light would shine forwards and then reflect back to you? If so, then light is travelling faster than the speed of light. Oh but hang on, it can't, coz it travels at the speed of light. Therefore, you travel through where you want them to shine at the same speed that the light shines at, so the lights won't illuminate things in front of you, therefore they don't "work".
cLive ;-)
*...let's forget about the time travel and infinite mass problems etc here for simplicity's sake!
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