In states that abide by the English common law liability theory of damages in automotive accident claims, if the damage was caused to your vehicle by another person, that other person is liable for the cost of repairing your vehicle even if you choose not to do so, because that is the damages that he did to your vehicle (the cost of making it whole). If, however, the damage was your fault, then it depends on what the contract between you and your insurer says, because then it is a matter of contract law rather than of liability law.
And note that if your Jeep is not paid off, you're out of the circuit depending upon your state's title theory -- in states that have a title theory of auto lien, the bank, not you, holds the title to the Jeep and the bank, not you, is the party dealing with the insurer to get the vehicle fixed so that if they have to repossess their property prior to it being paid off, they get a working easy-to-sell Jeep, not a rolling dent-up junk heap.
But none of this is going to get my steering box or bumper fixed, dudes! My shop is going to do that, and they need to know what steering box and bumper to order