Not necessarily as Verbo.......... I just did a kitchen in pale white oak, very reasonably all considered. It is not installed as yet, it's a new build. No more dollars, really, than any other higher end stain finish, and yes, slab door/drawer fronts and full overlay, which helps the cost

Not certain where you are located, but if NY, Pa. Maryland ? Pioneer in Lancaster Pa, can get you the look and pretty exactly that finish, they already have it from me and my pro KD. If you are? Message me @ Houzz

I'd highly recommend them. But you'd definitely need a KD and or Kitchen showroom somewhat near their Lancaster Locale, or a skilled KD who can work a longer distance relationship/make a new relationship.

I would add.......

Kitchens are layout !! appliances/ function/ storage, flooring/ cabinet finish/ lighting/ counter etc...........not usually just replacing what you HAVE and where it is. Lots of moving parts and pieces come together for a beautiful whole. If you want it right? Get very good help. PRO help.

https://www.pioneercustomkitchens.com/about-us.html

If you put in some planning effort to work with the cabinet sizes, get IKEA cabinets with third party doors from Scherr's. They have a wide selection of woods species, and cuts/grain types, they can also stain or paint for you. They primarily make their own cabinets, but if your pockets aren't as heavy with spare cash, IKEA + third party doors can take your kitchen remodel up a notch.

IMO buying doors from someone else and using IKea boxes saves not one penny the doors are what drives the cabinet price not the boxes. Either bite the bullet and get what you want and pay the price or choose another look you like. I use Ikea a lot for very contemporary kitchnes I do think outside the IKea box for design since Ikea can only design what is on the ir software . The only issue right now is everything seems to be slow for delivery so maybe check out a local cabinet maker who might have white oak on hand . Your inspo picdoes not appear to me to be anything special for the cabinets so maybe a cabinet company handles white oak as a choice

Cabinet pricing can be all over the board and so it is difficult to discuss prices on cabinets.

White Oak is expensive these days and rift-sawn is the most expensive White Oak, but that is not driving the premium that many cabinetmakers are charging. Veneers, even expensive wood veneers, are just not that big a portion of the total cost of cabinets. The marginal cost of rift-sawn White Oak in the kitchen pictured above isn't even $1,000 above a cheap veneer like Ash or Alder, and they are no harder to apply or finish.

Many cabinetmakers are just using a premium pricing strategy for rift-sawn White Oak. It is largely just a charge added because customers who want the product are willing to pay. If you look around, you can probably find someone not charging a massive premium for White Oak, but it may take some searching.

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IKEA is the cheapest Euro style cabinet frame I have found, but they have limited options available and may not work for everyone. I doubt you are going to find any other cabinet with Euro engineering and great hardware cheaper than IKEA even after paying for third party doors. Certainly, they are a better bargain with IKEA doors, but are a quality box at a good price without the doors.

You might find this thread helpful for a source.

https://www.houzz.com/discussions/5688207/cabinetry-brand-for-rift-oak-slab-cabinets

I have rift sawn white oak doors from Scherr's on IKEA boxes. In 2018, cost for both was just under $12K. I had Scherr stain and factory finish the doors. If I was willing to DYI, cost would have been less. Not a huge kitchen and it WAS 2018. But still....

If you've found a local cabinetmaker, suggest he look at white birch veneer ply and solid instead of rift cut white oak. Less expensive. More available. The look is close or better when compared to what you are really trying to get, which is French Oak. Birch is a hardwood which does not take dark stain very well. For light color finishes it works fine. French or European Oak are a different species than white oak. Without the open grain that turns black like N. American white and red oak unless you use rift or quarter sawn.