I never use primer, just two coats of paint.
I always use washable paint. The new ones are excellent, able to be washed with a wet sponge many times. If the paint is not washable, when you splat a mosquito on the wall, you can either leave it there, or scrub it off, but that also takes off the paint.
So, to answer your question: check if the primer you used can be cleaned. For example you can paint a spare bit of drywall, let it dry, then stain it with your favorite food item, and try to clean it with a wet sponge.
That will give you an idea of how your walls will look like in a few years. If you like the result, then you can save money on paint and apply the last coat in a few years, when it is needed. If the paint comes off the drywall and stays on the sponge instead, then I'd strongly recommend a coat of tougher washable paint on your primer... especially if it's in a kitchen. Thanks to the primer, it'll cost less, since you only need one coat.