Did you know that homeowner insurance (HOB-T) policy premiums are regulated by each state's State Board of Insurance Commissioners? Individual insurance companies can offer discounted rates (the practice is called deviating), which is why individual companies can each offer rates that differ from others.
For those who complain about the self-insurance deduction - on a replacement roof, for example - you can pay a larger premium to eliminate or reduce that self-insurance deductible.
Same for basic coverage: you can pay for the value of the house as of the date insured, or you can pay for "replacement cost" coverage. It's your choice, of course. But your plans for continuing to live in the house, or perhaps selling it in the near future, should impact that decision. Same rules apply to roof replacements, fence/gutter replacements, etc.
Finally, some insurance companies have the "nasty" habit of ceasing to write new/replacement business in a state after a round of natural disasters (tornados, hail, etc.). When they leave, you're often left holding the bag, because the next insurance company you deal with might be very reluctant to offer replacement cost coverage on (for example) your home's 17-year-old roof. By contrast, the carrier who continues to write your business year-after-year would be more inclined to continue to offer that replacement cost coverage.
The insurance agent is truly that - go-between between you (the buyer) and an insurance company. Independent agents deal with multiple insurance companies and thus can help you shop for the best fit. An agent who reps for only one insurance company is unable to do this.
Any insurance agent who attempts to sell you "only" on the annual premium, without first going through all of the variables, is NOT doing you a service.
My late father was a property/casualty insurance agent for 40 years. He taught me the messy details.