I think it's funny to have all this discussion over something I never considered to be an issue. I put on my gun (strong side OWB). I get in the car and drive. I can still draw it when seated, although not as easily as standing, but that's to be expected.
The practice of removing/replacing the gun with every entry and exit just creates opportunities for accidents and/or forgetting the gun at the wrong time. "Keep the gun on you" should be the rule.
If I am stopped for some routine traffic violation, I am not going to tell the officer I'm armed. I say this as a former officer of many years. Some cops will handle it calmly and be cool, others won't. I know my gun is not a threat to the police. He/she doesn't need to know. In some states, I guess you are required by law to disclose it, in which case you have no choice. But if you have a choice, there is no reason to do so. Just offer your license, registration and insurance, keep your hands on the wheel, and don't make a fuss.
What if the officer just straight up asks if there are any weapons in the car? You have to understand, many police are aggressive in their pursuit of making busts. They may ask all manner of intrusive questions, and may even ask to search your car. It is not unconstitutional for them to ask permission. But you DON"T have to answer, or give permission. Do not lie, but do not answer. My canned response to this situation is, "Officer, I'm happy to provide you the required documents, but I don't care to answer any fishing expedition questions." This may irk them. Tough. Just politely assert your rights, without being combative. If the officer oversteps, then you have an issue to resolve in court. Don't try to resolve it on the side of the road. You will lose.