I glossed over parts of this mechanism above, but partially pre-cocked strikers require the trigger bar to pull the striker back more before the trigger bar drops down, releasing the striker. The amount the striker is pre-cocked is not enough to ignite a primer, and the act of pulling the striker back against spring pressure mimics the sear geometry of a hammer fired gun.

Fully cocked strikers are ready to ignite a primer if the striker drops. I don't know of another design like Sig's that has a fully cocked striker, which is not to say there isn't one, or that they're all unsafe.

The P320 in particular suffers from compromises shoehorning a fire control unit designed for one gun into another.

Combined with poor manufacturing techniques, tolerance stacking, part mixing, and poor QA, the striker block, which is the last safety intended to block the striker without an explicit trigger pull, can become ineffective.

To answer your question, there's no mechanical reason a handgun cannot be designed an manufactured to not fire without explicit mechanical input from the user. Indeed almost every commercially produced handgun on the market fits this requirement. A combination of failures on Sig's part has allowed this to happen.