The laws of nature/physics have the same form in any inertial reference frame, maybe "the simplest" (do we all agree on the meaning of the word "simple"? And on the value of "simplicity"? I guess not) form, maybe not, but they have the very same form in all the reference frames (do we all agree that two equations are the same? I guess so).

To me, it's a pretty a valid reason to define inertial frames, and to test if we're in, or we're using, an inertial reference frame.

The laws of nature/physics have the same form in any inertial reference frame, maybe "the simplest" (do we all agree on the meaning of the word "simple"? And on the value of "simplicity"? I guess not) form, maybe not, but they have the very same form in all the inertial reference frames (do we all agree that two equations are the same? I guess so).

To me, it's a pretty valid reason to define inertial frames, and then to test if we're in, or we're using, an inertial reference frame.

See @Dale's answer for an operational definition of an inertial frame.