Ok, thanks, everyone, the decision has been made, we cut out that loop through Arizona and Utah. We had already cut Lake Tahoe earlier. The total driving time is much more manageable now and we were able to fit many two or three-day stops into the itinerary, which will allow us to explore and experience the places we are visiting.
The car comes with a complete package, BTW, that includes all insurance and unlimited mileage, so this would not have been the issue. It's always better to book rental cars from Europe to avoid discussions on what's included and what's needed.
We also added three nights in Laguna Beach to allow for some more beach time and a possible day trip to San Diego.