Weapon beside you on the seat or under your leg in the car is a fairly bad idea, panic braking, hard maneuvering, and that gun may not still be there. I think the Miami FBI shootout had a gun skittering across the floorboard unusable at the time. AIWB makes for an easy draw while seatbelted if you adjust accordingly.
Vigilant beat me to it. Seems he and I train in similar places and hold similar opinions.