It's true that there isn't really much of a discourse here in Germany about nuclear proliferation. But that aside, it would make sense, in a vacuum.
Geopolitically speaking, there are no such things as allies or friends. Neither the US, which has been proven to be irrational, unpredictable and unreliable, nor the French (naturally concerned with their own national security first and foremost) can be relied upon. "Verlass dich auf andere und du bist verlassen" comes to mind, ultimately you can only rely on yourself, especially with regards to interests and safety. And Germany is the only historically great European power left to nuclearize, after the UK, France and Russia. Thus the development and deployment of SSBNs, weapons of pure deterrence with little means of conventional warfighting outside of WW3 scenarios, based on a type of vessel Germany has lots of familiarity with, would make sense.
But ultimately, as already established, the will isn't there. And yes, the rest of Europe would collectively shit their pants. But the fact that a strategically autonomous Germany makes these supposed allies nervous, shows that they are not to be relied upon.
In short, SSBNs would be perfectly suited for German national deterrence and ensuring strategic autonomy and safety. But yes, there is no genuine discourse going on and nobody in high places is interested in the prospect. And yes, in the short term relations to some countries would sour.