Like most things in life, service matters to a point when it comes to cost, but after that point...
If Geico quoted me $100 for six months where I was currently paying $400 for a company I've had good experience with and trust to take care of me better than Geico if something happens, I'm probably not going to think much about switching for $300 even if that means paying 4x as much. If the difference was $1,000 vs $4,000 for six months, I'm not sure I'd say the same.