How cheap the free insurance quote you get is is influenced by your credit history. You will pay higher home insurance rates if you have a low credit rating. What your credit rating shows is how you have handled your bills and it speaks negatively about you if it is a poor one. An insurance company takes this to mean that you are not financially very responsible and will likely default in paying your rates. This makes you less attractive to them and you, therefore, are made to pay much more than someone else with the same profile that has an excellent rating.

Therefore, it will do you much good to clear all your bills once they are due. Apart from the other benefits in doing so, it will help you get  cheaper home insurance premiums.