Is it possible to explain the form of Lagrangian $L=T-V$ and action principle in the following way?

The force that acts on a mass particle is due to the potential $V(x)$. This force drives the particle to minimize its potential energy. We also know that the attraction is a negative form of potential energy. On the other hand, the Law of inertia implies that the mass particle tends to hinder acceleration and thus minimize its kinetic energy, but that increases the potential energy via force. During a process of motion from the point $x\_1$ to point $x\_2$ between times $t\_1$ and $t\_2$, the mass particle tends at every moment to minimize the sum of its kinetic and attractive potential energy, i.e. the term $L=T-V$. Also, when the integral is to be extremized, then if doesn't matter if we choose $L=T-V$ or $L=V-T$.

**EDIT**: We also know that a dynamical mechanical system tends to time-independent equilibrium $T=V$. If it holds that $T \neq V$, then the non-equilibrium state is a dynamical system that on an any time interval tends towards $T=V$, that is, to minimize the action. Now we see that if $T \neq V$, then the system clearly has some *equilibrium seeking action*!