Weird thing, I'm fifteen years in web programming with an interest in crypto, but it's the first time I hear that, at least in such categorical form. On the contrary, it's usually “public-key crypto allows you to have both this and that.”
There are things that make this less trivial to exploit for non-textbook cases. But, either way, it is generally easier to mostly go with “don’t use the same key for both signing and encryption” so you don’t have to do a bunch of stuff to figure out if a given construction is safe. If Filippo is supporting RSA ssh keys, I’d love a post walking through the way to prove that reusing RSA keys turns out to be safe if done carefully/thoughtfully.
In fact, TFA explicitly mentions an example of this causing a security problem[1]. In addition, not all public-key cryptosystems can be used to create both encryption and signing primitives[2].
[1]: https://eprint.iacr.org/2011/615.pdf [2]: https://www.cs.cornell.edu/courses/cs5430/2015sp/notes/rsa_s...