You need to use enough coats of primer so that the surface is consistent.
Imagine you are painting a chess board. After 1 coat of primer, you can still see the chess board. That is called "printing through". The layers of primer are not opaque enough to really hide it.
Note that if you are finding solids at the bottom of your primer can, that's because you did not mix the primer enough, and that will get you poor performing primer, since the solids are what makes it opaque! You can always take the can back to the paint store and ask them to shake it on their paint shaker.
The job of the primer is to equalize the underlying surface (in a number of factors, color is one of them). If the underlying surface is not equal, the primer job is not done!
Now I'll tell you a secret: 1-coat paint is a lie. If you try it in 1 coat, the primer color will "print through" somewhat. In other words if you painted a wall half 1-coat and half 2-coat, the difference will be obvious - the 1-coat side will have the primer color printing through somewhat. They're just hoping your application will be even enough that you won't notice lol.
Needless to say if the primer is not layered enough to make the surface totally consistent, that will immediately print through the 1 coat!
So I plan for 2 topcoats and n primer coats, with the value being enough to stop all print-through of the underlying surface. The last primer coat doesn't need total coverage of all differences (e.g. the chess board), but it needs to be close enough that the 2 coats of topcoat will seal the deal. Since I don't like re-doing jobs that failed, to me that means "pretty darn close".