Two other factors, in addition to those mentioned:
1. Car selection at an off-airport location may be severely limited. Not only in size or model, but you could end up in a car with very high mileage with no ability to switch.
2. Car return. Many off airport locations have very limited hours. And, you might not be allowed to return to the airport without a significant drop charge, negating any imagined savings in airport fees.
The LAX facility is guaranteed open 24/7.