By "real" I assume you mean solid boards of wood. These aren't normally used for speaker building because of inconsistencies from one board to the next, possibilities of warping, cracking, or shrinking if they're not fully dried and protected from humidity, and cost.
Plywood has none of the above problems, or at least significantly less of those problems, and is easier to work with.
As to your question, sure, you could just build a new set of cabinets, but the time, effort, cost, tools required, skills required (if you're not already an experienced woodworker) makes that a lot of work as opposed to simply re-veneering the existing cabs, as long as they're reasonably solid. However, the resulting value would, essentially, go straight down to the value of the drivers as parts. Because that's what you'd have, a set of AR drivers in non-original wooden boxes.
And veneering is fun, and you can wow your friends with the results!