No, I don't think it necessary. I don't really have an explanation, but I don't think you need to go through the trouble.

Is there a reason why you do not want the beds or the plants to have contact with the dirt below ? The recommendation usually is to put down cardboard or several layers of newspaper, wet them down, then place the bed on top and fill. Eventually the paper will break down and the roots of your veggies will be able to reach down into the soil below if they so desire. Also, the worms below will be able to come up into the bed.

My thought in putting down brick was just to extend the life of the wood. I'm using cedar and it is sealed, but it wasn't cheap and there is some work into it. So I want them to last as long as possible.

There is no reason for weed cloth if you are putting over soil. In fact, I can find no reason to do so. So that would eliminate the need for bricks.

Dan

Isn't Cedar naturally resistant to rot and insects? Aside from becoming a beautiful grey when it becomes weathered.