> You will have a hard time using theory to justify that SAT is easier than any other NP-complete problem

"Easier" perhaps isn't the right word (in terms of reducibility, it certainly isn't), but FPT is just a way to demonstrate that NP-complete problems can be different from each other in ways that matter (with respect to "natural" instances).

> Now, take a cryptographic instance, translate it into a CNF formula and call a SAT solver, I doubt it will shine.

Exactly. And researchers are very much interested in these differences that arise in natural instances and are hidden by "crude" reduction.