It would likely be far more cost efective to use the curent flat packs and have them laminated after assembly. I'm not saying it can't be done but hardwood is expensive and it can be more prone to resonence
Do you have a particular type of wood in mind ?
Something to keep in mind about hardwood is that it comes in varying size boards, not sheets like MDF. You would have to joint the edges flat and square so you can glue the pieces up into panels of the size you need, keeping grain pattern in mind for flow to adjacent pieces. Then the panels will have to be planed to a uniform thickness.
The width of the panels is going to be limited to the width of the planer which is going to be somewhere between 12" and 25" (my planer is 15"). The only way to get panels wider than the planer is to glue up multiple individual panels to the width of the planer and glue these panels together. Then you have to use hand planes to flatten, smooth and thickness the large panel to it's final dimensions.
Since the widest piece of the MTM Otica is the big wing at 20" you could do it with access to a 24" planer. Again be careful about grain direction. You would want it to match as it wraps around the big wing, baffle and small wing.
Another issue with solid wood to keep in mind is movement. Solid wood is not stationary. It expands and contracts with seasonal moisture variations. This movement occurs across the grain. To make the cabinet look right the grain would be oriented vertically. That would mean the expansion and contraction would occur across the width of the piece. Being glued to the base the bottom would be constrained but the top would be free to move. This would likely cause the wood to crack. One way around this would be to screw the wings and baffle to the base in such a way the bottom could expand and contract.
Another option would be to use a wood that doesn't expand or contract much. Usually that means quartersawn lumber. The issue is that the grain pattern on most quartersawn lumber is rather blend. For the most part, the really pretty grain patterns occur in flatsawn lumber but flatsawn tends to move the most in response moisture. There are exceptions to everything though. Highly figured quartersawn white oak is stunning while flatsawn mesquite is very stable.
As for resonances, at least with the MTM version, I wonder how much of an issue it would really be given how open the design is only the big wing should be affected and it has NoRez on the inside.
I'm not saying it can't be done, just that there is a lot more to doing it and making the end product look right than most people realize.