I would think twice about this, because your insurance company has contractual obligations to you based on your policy. I had a case where the driver's insurance company limited rental and replacement costs on a totalled vehicle to his policy limit. I had to directly engage the at-fault driver's insurance company to get anything close to a reasonable amount to compensate and replace the vehicle.
My recommendation is to always go to the at-fault's insurer, as that relationship legally requires that insurer to make you whole. (A LIKE-Rental vehicle [not POS ICE] for as long as it takes; if repaired, you should get compensated for the diminshed value the car will have when you sell it; if totalled, ensure you can get a LIKE Tesla replacement - similar mileage, features, and age.) Your own insurance, for example, will be studiously uninterested in pursuing diminished value or even informing you of your right to same.