I recently bought a house with white washed oak cabinets. They looked just like your pic. They were prey dirty and seemed very porous. After a coat of shellac primer and three coats of oil paint, they are no longer that way.

I would not do a white wash, unless you plan to coat with matte poly. General finishes high endurance is great.

Mine were a different color and in a bathroom not a kitchen. I loved the look for the same reasons you mention and never had any issues. If they are factory painted with a catalyzed finish, they should hold up well.

If you use a professional grade 2K poly or conversion varnish product, it will be fine.Homeowner box store products, craft paint, and kludges as a substitute for a poor process or product , wont.