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While I have no idea if you are right or not, don't you think that attempting to improve where other's have failed is potentially worthy of many tries? Especially if there is no fundamental proof that something won't work? And even more when a real unsolved problem is attempting to be solved?

The analogy to reinventing the wheel is inappropriate, since in the case of a working solution, it is a waste of time to reinvent it. But, in the case of failures, "reinventing it" (and potentially no longer failing), should be praised, not ridiculed, no? (again, with the proof caveat above, and even then some... proofs can sometimes be disproved)