Should you run a car without a thermostat?

I know I can't run one in my set up. When I first bought the car I pulled out the restrictor and put in a T stat. Every time I ran the car and shut it down the upper radiator hose would collapse. Found out the hard way that with the electric pump there is no recirc line so when the T stat is closed it dead heads. I run my car on the street to local cruise ins and such with a restrictor and don't have any issues with it. The highest temp I've seen was around 190 or so on a hot day with prolonged driving.