Does Inertial motion really exist?

Answer 1

I found no reference to "inertial motion." Did you mean inertial mass (m)? There is also the concept of motion in an inertial frame; perhaps that's what you meant. [See source.]

An inertial mass is simply one that fits into the equation F = ma. (There is also a gravitational mass that fits into W = mg; where W is weight and g is the acceleration due to gravity. Einstein claims the two masses are equivalent.) Because F = ma has been proved over and over again, even in high school labs, I think it's safe to say that m does exist.

The conservation of energy and of momentum laws are two major uses of inertial mass. These two laws have been proved over and over again; this also validates the concept of inertial mass.