The arm (or whip) would still have to accelerate from 0 to ~2000+ rpm on half a revolution even though its flexible. So there would still be enormous accelerations even though the whip eventually partly smoothens out the peak acceleration. it would be more like a collision which in turns introduces higher stresses (and probably vibrations too) to the system. Both requiring you to increase the strength + rigidity of the system and hence also increase weight on the arm. Which in turns increases inertia and the "collision" effect.

Not saying its impossible to create a successful system like that, in fact it sounds sort of a natural/organic design that potential could be closer to the optimal design, but it would be more difficult to accomplish and probably need more testing and design iterations. So I think OPs strategy is more simple and pragmatic in this case.

One could test this manually with a whip, right? Attach the ball at the end and try to crack it.

Nothing above absolute zero is fully rigid.

You're going to transfer the energy quickly, you'll just break any "arm" that's light enough to accelerate with the energy available.

You could maybe use an 'already broken' arm (rope, like a whip) but then it's not a trebuchet.