Don't think gun, think numbers
I know that from a police perspective the insurance companies want us to use rifles that were purpose built for l.e. or military application. The insurance company does not want the SWAT team Marksman Observer using his favorite varmint rifle.
And just what does an insurance company know about shooting? Squat, generally. Here's what I think (no proof, just opinion)
Insurance companies are all about numbers. EVERYTHING is given a number, and plugged into their equations to determine amount of risk,
to their money.
I think they get their knickers in a twist over your "favorite varmint rifle", because it is an unknown variable. This upsets their calculations and anything that does that increases their risk for having to pay out. I think purpose built LE & military arms are considered by them a "known quantity", so they can be given a standard number, where needed, for their risk calculations. And having to create a "valid" number for that, for each and every individual rifle someone might use means, at the very least they have to do more work (more cost to them) to figure out the "proper" assessment.
Much simpler, easier, and cheaper to insist on a "standard" that they can use.
I'm quite confident my Win M70 Varmint in .22-250 can do any job any .223 can do (other than rapid fire/suppressive fire), BUT its not something the insurance companies can easily quantify, so they would not like me (or you) to use it. And since they are the ones providing the insurance, they get to call the shots, so to speak. Handloaded ammo would be out, too, for the same reason.