The only reason I wouldn't mind a higher score is because I hear insurance companies and some others charge customers less when they have higher scores. I have no experience with this happening to my knowledge, especially since it seems to be a secret.
Insurance have their own score models, but they closely mirror and use much of same data as a fico model. If your FICO (fico 08, not vantage or whatever) is > 760, you're probably already effectively in the top risk tier - much the same way it works with mortgages...
I do make it a point, whenever doing any insurance changes, to always mention that my credit score is high - and set the expectation, beforehand, that I am low-risk, happy to pay 6mo or 12mo upfront, and that I am very much "shopping" and free to walk at any point.
ETA: You'll note that that means that I don't do insurance shopping online and still use human agents, when possible. Better deals - at least so far - and more ability to negotiate down. The online joints charge millennials more because they can't talk on the phone!
