I had never driven on the beach with my car before but it seems like this is the way they do things here in Texas. I have to admit it was kind of nice to have our car on the beach because it gave us a nice shade and we had all our supplies nearby. However, a car with four wheel drive is highly recommended, because you don't want to get stuck in the sand!
By all means bring your umbrella or tent, or stop by a souvenir shop and buy one. The sun is strong and mega hot, especially in these dog days of summer. Since we are in the middle of summer, the beach was busy but definitely not as crowded as it gets on Isla Blanca. Luckily, SPI is not that long or big, so it really is a 15/20 min drive or so from the bridge to Beach Access #6 (depending on traffic).
What's your local beach like?