You're making the point here. It's the software that makes our lives significantly better, which is the most important one.
However, as software is everywhere, the original question is the same thing as "what physical invention" is the most important one?
From one standpoint this could be something like the wheel or electrical light, i.e. Bios, compiler or a network stack in the software world. Or, something way more personal, like health care related software for the loved ones or some more profane stuff.
To make the question even less tangible, software in general can be replaced more easily than physical things, most of the time.
highly classified stuff, but in its day likely a FORTRAN implementation, the OPLAN is not simply a computer program but is a heuristic of human operations that is modified depending on current intelligence briefs, and asset deployment and distribution. The ARPANET [DARPANET] was a major part of this.
I had a teach who once was reviewing the history of computing. She explained how time sharing was invented in the 1960s. The ability for a computer to do more than one thing at a time, was a HUGE improvement.