Are there historical examples of Occam's Razor being useful to cryptography research?
The definition you cite says that "among competing hypotheses, the one with the fewest assumptions should be selected". If you take this literally and don't understand fewer assumptions as simpler, this principle is widely accepted in cryptographic research: Having a provably secure scheme means that it can be shown to satisfy some security definition under certain assumptions. If you propose a new scheme and prove its security under weaker (or less) assumptions than what was needed for previous schemes, this is considered to be a substantial contribution.

As an example, consider RSA. A necessary assumption for RSA to be secure is that factoring is hard. However, nobody has succeeded so far in proving that under that assumption, RSA is actually secure. There exist security proofs for (variants of) RSA, but they require additional assumptions. At Eurocrypt 2009, a paper [1] received the best paper award for proposing an encryption scheme that is provably secure assuming only that factoring is hard. That scheme is not simpler than RSA, but the hypothesis that it is secure can be based on fewer assumptions.

[1] Dennis Hofheinz, Eike Kiltz: Practical Chosen Ciphertext Secure Encryption from Factoring. EUROCRYPT 2009.