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Yeh it looks like a terrible design for rigidity in that plane, it's got 0 bracing for it. Must be quite strong in the opposite direction!
But yes, the solution to this is more about bracing the structure properly. It would be quite basic maths to work out what the approximate bending loads must be to be causing 40mm steel tubing to deflect, and then from there it won't be hard to work out that to make it sufficiently strong with carbon shells is extremely inefficient. What it would cost to make those shells vs what it would cost to weld in another steel bar, its a pretty obvious choice.
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