As far as I can tell the primary purpose of a primer is to identify areas that need more work. Primers are generally easy to sand to allow you to fix these problem areas.
Anytime I talk to my rep at sherwin williams they seem to indicate that you can use an initial coat of any paint as a primer. The initial coat will seal up substrates. Using a paint as primer is typically not ideal as it won't sand well. Obviously if you are going over oil or sealing out mold or stains then you want a primer designed for that and you'll sacrifice sandability.
In your case if the paint job looks good then you are probably ok. The other thing a primer is probably better at doing is handling the initial layer of drywall dust left from sanding - depending on how good of a job you do cleaning your walls after sanding. A lot of pros don't clean the walls after sanding and rely on PVA primers to handle the residual dust on the wall. I am not sure how paint vs pva primer preforms when absorbing and bonding to dusty drywall.
I have heard of these primer with paint mixtures - so they either make a hard to sand primer or a easy to scuff/damage paint? Doesn't seem like a great idea.