Costco does sell cabinets and you can buy kitchen and bathroom cabinets from Costco. None are in stock in stores, they must be special ordered and Costco offers curbside delivery. It is up to you to self-install your cabinets or to find a professional to do it for you.
All Wood Cabinetry
Modern bathroom and kitchen cabinets are very rarely made of pure hardwood, through and through. Not only does cost prohibit this, but solid wood is at risk for warping and splitting. Wood products perform far better. AWC cabinets are comparable to other cabinets on the market in that they are largely composed of furniture-grade plywood, MDF (medium density fiberboard), and wood veneer (which is 100% natural wood).
This is common practice with bathroom and kitchen cabinet manufacturers. Lower-quality cabinet cores would be made of medium-density fiberboard, also known as particleboard. AWC does state that only one cabinet line, Hamilton Arctic White, is this MDF core with wrapped thermoplastic veneer.
Costco Member Discounts
We looked at a 24" base cabinet, oak veneer, as a point of comparison to other brands. This cabinet is both 24" wide and the standard 24" deep and 34 1/2" high. It has one drawer on top, two doors on bottom, and works well in either bathroom or kitchen.
The stated price was $345. With Costco membership, you shave off $138 for a total of $207. At the time of this writing, Lowe's was offering an oak 24" base cabinet, one drawer and one door, for around $50 less. But the material was MDF. Home Depot also offered a similar oak cabinet for around the same price as the Costco/AWC cabinet, but again: MDF construction.
Other solid-wood offerings nearer to the construction of the Costco/All Wood Cabinetry (AWC) run around the same price as Costco/AWC's or slightly higher.
This is a decent price. Costco/AWC was also throwing in soft door closes and drawer extensions for free as a part of the promotion. These aren't a huge deal, but nice to have (and if you're buying kitchen cabinets from a local retailer or used, you bet they will throw these in as an incentive).
The Bottom Line
Costco cabinets are a good deal, but they are not a better deal than RTA cabinet companies. If you are willing to assemble your own cabinets—which is far easier than it sounds—you can't score a better deal than with Costco. If you are not already a Costco member, it would not be worth buying a membership simply for their kitchen cabinets.