Here's what you do without, on the negative side, just for balance:
A bill: When I last had comprehensive insurance, it cost something like 3-4% of the value of the car per annum. (Obviously ymmv enormously but I think that's somewhere near the middle of the range and I'm not especially risky.) So, compared to the total depreciation and running costs of the car, it's actually fairly substantial. Over the say 10 years I might keep that car, it adds up to a fair slice of what it will take to buy a replacement.
Financial crisis costs: I don't know about you, but my insurance went up something like 30% in recent years, despite the value-insured and the risk going down, said by the insurer to be due to market turmoil. So, at least hundreds of dollars is just kind of frictional loss, and I'd rather not pay it.
Wrangling with the insurer: if you have insurance and a loss, you have to persuade them to pay out, perhaps document the original conditions or the fault, perhaps argue about whether their payment is fair. I've done this for small (non-automotive) claims, and it added up to more hassle than the incident itself. Obviously all insurers will claim they're friendly to deal with but until you actually have a big claim you never know.
Moral hazard: I know I'm solely responsible for not having my car crashed or stolen. Somehow that just feels better.
Free riders: I've seen people "fudge" their insurance claims so that things that shouldn't have been covered were claimed to be. You might have too. Buy insurance and you're paying for them.
Choice: Insurers are typically going to make the decision for you about whether a claim is repairable or not, and in my experience are reluctant or refuse to just give you the cash amount of the claim. (See also, moral hazard.) Do it yourself and you can choose whether to live with it, make a smaller or larger repair, or replace the whole vehicle with a second hand one or a brand new one, or indeed perhaps do without a vehicle.
A distraction: Hopefully by the time you've been working for a while, a vehicle is not a really large fraction of your net worth. If you lose 10% of your net worth it's not really nice but - well, you could easily have lost that off the value of your house or your retirement portfolio in recent years. What you actually need to insure is genuinely serious risks that would seriously change your life if they were lost, such as your ability to work. For about the same cost as insuring a $x car, you can insure against $x income every year for the rest of your life, and I think it's far more important. If I have a write-off accident but walk away I'll be perfectly happy. And, obviously, liability insurance is important, because being hit for $millions of liabilities could also have a serious impact.
Coverage for mechanical failures: If your 8yo car needs a new transmission, insurance isn't going to help, yet it may cost more than the typical minor collision. Save the money yourself and you can manage those costs out of the same bucket.
Flexibility: If you save up to replace your car, but some other crisis occurs, you can choose to put the money towards that. If you have car insurance but you have a family medical thing it's no help.
I think the bottom line is: insure against costs you couldn't cope with by yourself. There are people who need a car but can just barely afford it, but if you're fortunate enough not to be in that case you don't really need comprehensive insurance.