Address reuse only becomes a problem in the theoretical case that someone can determine the private key from a signature. This would only happen if there was some sort of breakthrough in cryptoanalysis of elliptic curve cryptography, which while theoretically possible, is unlikely.
The idea is that you don't want to be secure now, but also in the future. The ECC Bitcoin uses is vulnerable to Shor's algorithm, and thus quantum computation. Quantum computing at that scale is a fair ways off, most likely, but on a timescale of a couple decades or more, a successful attack seems quite reasonable.
Bitcoin can soft-fork, allowing address generation with a different algorithm. It's not any sort of existential threat to Bitcoin. But it does require that you move your coins to a new address if you reuse an address, else you are vulnerable.
Not to mention, that such a discovery would be significant enough - that a protocol upgrade and fork would be inevitable, in order to protect addresses retroactively.
