I'm still hung up on the argument of "You should only be paid the amount that the car decreased in value, not how much it'd cost for a licensed mechanic to restore it to the same condition it was in before the accident."
Ok, how about this. It's either-or. Whatever rule you come up with, EVERYONE has to abide by. So either everyone only gets paid the amount that the car has decreased in value, or it gets fixed to the same condition as before the accident. No getting to choose for yourself.
Let's assume you pick #1, you only get paid the amount that the car decreased in value. You have a brand-new car that's financed (not frugal, but not illegal/immoral either). You drive it off the lot, now you have a $15,000 car with a $20,000 loan. Someone rear-ends you, and the value decreases to $10,000. Assuming it works like I think it will, that means the insurance company will cut a $5,000 check to your finance company. The car is undriveable as-is. It'll cost $7,000 to fix it (heck, wouldn't matter if it was $3,000...you don't have the spare cash anymore). So now you have a $15,000 loan on a $10,000 car you can't even drive.
Or let's say you have a $1,000 car. Someone hits you causing $800 in damage. But the scrap yard would gladly give you $500 for the car. Hey, that's not bad...insurance will give you $500, scrap yard $500, you just sold your car! But you didn't want to sell it, you took good care of it, and it's mostly cosmetic damage anyways. To keep the car, you have to take the $500 and pay the extra $300 out of pocket to get it fixed (this is assuming you're not a shade tree mechanic, and willing to take it on yourself).
In my view, if anyone is going to come out ahead, it should be the person who's NOT at fault. I'm not saying they SHOULD come out ahead...but rather, if it's going to be them OR the person who was actually negligent, I'm picking the innocent party.
The existing system isn't perfect, but it's fair for the most part. If you're in an accident and it's the other person's fault, they're liable to pay to get your car back in the same condition it was in before the accident. They won't pay for just the parts, or make you learn how to do it; rather they'll pay an appropriate amount for a (semi) reputable mechanic to do a proper repair. If the repair costs more than the car was worth, then they'll "total" it and give you a "fair" amount for what it could have reasonably been sold for. The liable party can not insist that you use a specific mechanic, but they can require multiple estimates and require that the car actually be repaired (i.e. they pay the repair shop directly). If they cut you a check, it's to do what you wish with; repair the car, sell the car and combine the funds to buy a new one, buy a robot butler, whatever.