First.. Yes, sadly I used to work in insurance..
And sadly, your premium will be going up either way, though slightly more if you file a claim, but worth it to file a claim.
Insurance is done by groupings (streets, blocks, subdivisions, cities, metros) if anyone on your street/block... has a claim, your area goes up in risk, possibly only fractions of a penny, the more claims, the larger the claims, the higher the increase. All of the insurance companies breakdown the areas slightly different but use the same general idea. (It is possible for the people across the street to fall into a different grouping, think school districts).
You should have your insurance company come out and do an inspection. They will give you a dollar amount offer if the damages are bad enough. If they say only $1000, gladly thank them and decline to proceed with the claim (your roof is not that bad). Inspections and starting claims do not raise your rates. If they offer you $3-6k. Replace it, your premium will go up but it will take years for it to equal $3-6k (if ever).