Depends on a lot of factors… I’m assuming you are under 25, so your rates will probably go up quite a bit.
Evaluate from a cost standpoint… If the damage is 4k, then assuming your rate goes up by 150 a month (pretty big amount but hey it’s a guess), then it would take 4000/150, or about 27 months for the increase in insurance to “cover” that payment.
That’s all just a guess but you can see where I am going with this.
If the increase in rate is substantial, think of how long it will take for it to reach 4000 in damages. If that length of time is longer than you intend to keep the car, then have insurance cover it and suck up the estimated increase…
If you intend to pay the 4000 up front to avoid going through insurance altogether, be sure to include the true cost as in any interest you pay in loans, whatever if you are borrowing that money to have it repaired.
That being said, 4k is a pretty big chunk to eat up on your own… Yet with your recent crashes insurance may really go up a lot too. Best of luck…