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This sounds like sort of reasonably OK layman's explanation of Weak DH https://weakdh.org/

Except that Weak DH only needs one prime - not two. It sounds like the author conflated RSA with DH somehow. It's very rare for real in-the-wild RSA keys to share factors (barring stupid errors like Debian's randomization fail).

Not as rare as it should be (see https://cryptosense.com/blog/more-weak-rsa-keys-in-network-d...) -- but there are much easier fixes than QKD.

It doesn't.

Also the solution to weak DH is certainly not qkd. It's not using DH with weak parameters.

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