Is it necessary to put a primer on if the paint contains a primer?

Many have stated they had to use both as the paint and primer in one did not cover.

I recently painted all of the bedrooms in our house, both light and dark colors, using paints from Sherwin Williams that had the primer built in. I still had to do at least 2 coats, if not 3, on all of my walls. So, I think it depends on how porous the walls are as to whether the paint really sinks in or adheres, and also depends on the color you are going over, and what color you are painting with. So, just be advised, that even with a built in primer, you may need to do more than one coat anyway.

All the TV ads claim one coat coverage. Look at the ads carefully and the rollers are loaded with paint. So much that the paint even leaves a texture. Who does that?! There really isn't any "primer" in the paint. They just have more paint solids in them and a high price. I tried them, don't like them, don't use them. I still prime with a stain blocking primer then paint. The final finish is brighter and the color more vivid.

I think it's easier to just prime first. It's hard to find good thick paint these days

Absolutely use a regular primer first or you'll be spending more money on the paint with primer to cover the walls. And DON'T put your paint on thick. Use several thin coats and it will never peel.