I almost always fished at La Jolla alone. Nearly every time I went out, I had camera gear and a radio. I always kept my rods and gear below deck while I carted my kayak to the beach. I took the cart back to my truck and picked up my expensive and easy to steal gear and took it down to the beach immediately before launching.
La Jolla is a ritzy place, but popular at night with the non-ritzy crowd; especially around the bathrooms by the main parking lot. That's part of the deal, gotta keep on your toes.
Of course, you can lose stuff just about anywhere.