Issue repainting existing cabinets on flip. Is contractor right?

[Katie Neason]

I am on my 4 SFR flip. So I have just enough experience to think I know more than I do. We are repainting the existing kitchen cabinets. According to the painter he has put 4 coats of primer and 2 coasts of paint (whitish color) and the wood grain color is bleeding through. He says the issue is that it is a wood grain skin/veneer. He wants me to pick a darker color. I would prefer not to and am skeptical. He is using Home Depot's Glidden Pro Paint. Before I do I want to get options from others who have experienced it. Here are some pic before and after. Thanks!

[Andrew Cordle]

I have redone a ton of oak cabinets in my flips. 

The best product I have seen is by Rust O Lem and it is called Cabinet Transformation.

You can pick out tons and tons of colors its super simple and for me never bleeds through. 

Here is an example.... These looked just like what your originals ones looked like. We sold this property for around 190k.