The idea of a mixed primer and paint combo is for sales and not for lasting results. All paints will stick to a variety of substrates without a primer; Example- Painting the outside of your home. It is in overall good shape and just faded. All that is needed is a good washing, minimal prep and good paint applied.
Read the can label. You will find each manufacture recommends specialized primers for different substrates. The best question is; Why recommend using a primer when the fancy paint label says "Paint n Primer?"
Primers are specially formulated for specific substrates and specific top coats. There are many types available. The best approach is to use one of these primers, best one for your situation, then top coat with a good paint. You only have 1 chance to get this right, using a good primer is recommended for lasting results.