This is a downfall of dealing with a bank/direct writer/insurance agent. They can only propose coverage based on the rules of the single company they represent. So you may hear, "full coverage is not available because your car is too old". Do not take that as a blanket statement which applies to all insurance companies. If you are being told you can't get the coverage you asked for, the next question you need to be asking is, "is this coverage available elsewhere in the insurance market". Then call a broker. We ("we" being insurance brokers in general) represent multiple companies and can likely find you a policy with all the coverages you want.
I'm not an agent but my take is there are considerably more advantages to being friendly with your broker as opposed to xyz insurance comp. My broker can bind insurance over the phone at anytime of the day. It's unlikely that an insurance company will do this for you. Brokers are also working for you so when you get into an accident and you don't have a broker between you and the insurance company it's you against them, and they really don't want to pay you. For my money I am going to be supporting my broker for the foreseeable future.