Your three-layer roof is definitely a potential structural concern, and homeowners insurance companies might consider three layers of roof shingles. According to the International Existing Building Code, homes can be re-roofed one time by applying a second layer of roof shingles over the existing one, but after that application begins to wear, both layers need to be removed before a brand new roof is installed.
There are important reasons why this code is in effect. For one, a layer of shingles adds considerable weight to a roof─weight that can be hard for a structure to carry when severe weather strikes. Second, the fasteners used to hold shingles in place need to penetrate through to the the roof sheathing under the shingles, and if they damage underlying layers or pop or tear the new shingles along the way (a phenomenon worsened when the roof heats up), the integrity of the roof is impacted.
Additional guidelines may apply depending on where you live, and as stormy seasons approach, the Institute for Business & Home Safety recommend that those in high-wind areas have all old layers of roof shingles removed before reroofing, as working off of clean and sturdy roof sheathing provides much more dependable results.
So, I'm afraid the costs are going to be high whether the existing three-layer roof is insured or replaced. The size and location of your home and available options in roofing materials may still make the latter possible for you, so get estimates from a few reputable roofing contractors.
You'll then be better able to weigh the cost of having a new, safe, easily insurable single roof layer against paying a high premium for the multiple roof layers you already have.