Why personify crypto? Let the math alone be the driver in this domain. What is solid and true will eventually trickle up.
Unless you have some way of proving that one-way functions exist, which would imply as a consequence P ≠ NP, this is literally untrue (unless by "eventually" you mean "one day centuries hence, maybe we'll prove P ≠ NP"). There is not a single piece of crypto that can be proven correct today; all crypto that we use is safe because mathematicians have so far been unable to find a practical way to break.
This requires mathematicians to be actively trying to break the crypto, so personalities matter because you can't get a worldwide community of experts to study every random person's algorithm. This also requires mathematicians to have a sense of which ways a particular algorithm might be fragile, even if they can't break it quite yet, which requires some non-mathematically-provable trust in the cryptanalyst's good sense.
And, of course, if you believe that a certain cryptographer might be inserting back doors or prone to approving crypto that has back doors (see for instance Dual_EC_DRBG), you might distrust other output from that same cryptographer even if you can't prove anything yet.
Also good luck finding a nonce-reuse resistant algorithm.
The failure modes of reusing a nonce are never good, but some are far worse than others. The one-time pad's failure mode is particularly disastrous; it leaks the XOR of two plaintexts. There are a good number of algorithms that only leak whether the same message was repeated.
Not that I know of. As far as I know the security reductions are unconditional.
Even worse than revealing the XOR of 2 plaintexts is the key recovery enabled by GCM (source: other comments in this thread). And if you're that scared of nonce reuse, just
Nevertheless, it doesn't matter. Avoiding nonce reuse is easy. And if you're really scared, just use a random nonce from a big enough space (192 bits, like XChacha20, are good). That way if you have access to a random source, you can turn any encryption algorithm into a nonce-less algorithm.