The basis of homeowner's insurance pricing is the AOI, or Amount of Insurance. This pertains to the cost to rebuild the dwelling in the event of a total loss. The standard coverages (e.g., contents, loss of use, medical payments, liability) are calculated relative to this amount. Consequently, the AOI is selected by appraising the value of the dwelling. This is why it is important that if parts of the dwelling are upgraded, that the cost of those upgrades are taken into account.
The question is not one of denying claims should a loss occur, unless the nature of the upgrade is such that policy should not have been underwritten in the first place. (This can happen if, for example, the homeowner builds an extension onto the house that damages the structural integrity of the dwelling.)
In the end, the AOI is still just an estimate, but the takeaway is that, like scheduled personal property, jewelry, rare collectibles, or other endorsements, every home (and homeowner) has slightly different insurance needs, and it is in your interest to tailor your coverage to be as accurate as possible in reflecting your needs. Insurance is not a one-size-fits-all product; consequently, the selection of sufficient coverage for your mix of risks is only prudent. Now, if after you get a quote back and you find that the premium is too high, you can typically select a deductible that can reduce it, but you have to consider what amount of exposure you are willing to retain. You should shop around, too: different insurers use different methods and criteria to price their products, so even if the coverage is substantially similar, the premiums may vary: for example, some insurers ask whether you own a dog (exposure to liability claims), but others do not. Some insurers put more weight on your dwelling's geographic location (exposure to fire, theft, wind/hail) than others.