Have I missed any reason or benefit to keep the full coverage?
There is one that you might not have thought of, and nobody has mentioned yet. Unethical people.
I had one accident where the other party was clearly at fault. In fact, they said so when we exchanged details, but that his insurance company would reach out to mine to take care of it. I mentioned they should reach out to me directly, as I wasn't insured. He went radio silence, called up his insurance company, they said he never lodged a claim or admitted fault. He didn't take any calls, wouldn't respond to any emails.
I had to lawyer up, and the day before the statement of claim said we were going to lodge, he replied he called the insurance company and said he wasn't at fault, that I rolled back into him, he didn't run up the back of me, despite the unlikelihood of that. Even the insurance company, figuring that he was privately retained, played the same games. Requested we get multiple quotes, and finding trivial reasons to reject them, knowing each time they asked for something else, I got billed by the lawyer again, hoping I would figure it's cheaper to pay for my own damage. Whereas with an insurance company lawyer, they are salaried, and will try to reclaim the money, going straight to court if they have to, and the judge will see any poor behaviour.
They didn't know the lawyer was a friend acting pro-bono, or rather for BBQ and a beer. He let them play their game for a while, then said "I think I have enough evidence you're not negotiating in good faith. We'll see you in court X date". We got a settlement check for the cheapest quote that afternoon.
People who know you aren't insured, will try to screw you over. That's something an actuary doesn't calculate into your premiums. It's not worth the hassle to go through that, unless you too have a friend who will do pro-bono work.