> I'm not a cryptographer - but I don't think there's anything wrong with XOR encryption
When cryptographers and security professionals talk about XORing the keystream output of a pseudorandom function with plaintext to encrypt it, we don't call it "XOR encryption", we call it a stream cipher.
When we talk about XORing with a random pad of equal length to the plaintext, we don't call it "XOR encryption", we call it a one-time pad.
When we say "XOR encryption" we invariably mean "silly insecure thing with a repeating keystream no longer than a few bytes".
> XOR with a sufficiently large key is absolutely fine
It isn't. XOR with any key ever used more than once or looped around isn't not just "not unbreakable", it's demonstrably insecure. There is no "sufficiently large key" other than "same size as the plaintext and used only once for that plaintext" (a one time pad). To use smaller keys you need real cryptography, not XOR. Military radios absolutely do not work like this. They use stream ciphers, which can produce ~arbitrary length keystreams without repetition from a small seed key.