Information about what you're willing to pay isn't sufficient to lead to you paying a higher price, like in your example. There has to be no competition in the given market (probably not the case in your particular example-- car insurance).
So, if an insurer can identify that you have a greater risk than your friend, in perfect competition you would pay a higher rate. No insurer with perfect knowledge of risk would allow you to pay less than that, because they’re expected return would be negative.
In that case the companies will compete to give you competitive yet higher than others quotes to YOU(as they can see).
It's not about "lack of ability to advertise", it's about someone being able to heavily manipulate the perceived availability of competition (which is much more important than the real availability of competition). And that someone is the same someone that helps the companies manipulate the price (hint: it's Google).