Hot take.

I was wondering about this simple law yesterday,

when the force is constant, it gets simplified into

What got me thinking was the importance of this physical quantity such that it needed to involve 2 of the most fundamental physical concepts, Force and displacement.

Classically and logically, force had always been associated with change in momentum. From Newton's second law, $\vec{F}=\frac{d\vec{p}}{dt}$. Under conditions of constant mass (non-relativistic mechanics), the famous F = ma relation drops out.

The problem is not with force, it's with velocity and that is pulled over into all physical quantities including work and power. The problem is that we have a fixed span of time in our life. While velocity is a natural kinematic property, the view changes when it comes to us. Us creatures, who have a time span.

The importance of time, naturally develops the instinct to fulfill our needs in the least time possible. That sort of puts us in God mode, as in we are controlling the time it takes for something to happen.

That is the reason for velocity. Our need is covering a certain displacement which is fixed, so we tamper the time so a body with more velocity suits us more than a body with less velocity depending on the circumstances. In fact, that is why the power of a body is more important that the energy it possesses.

For energy is such a thing that is omnipresent, it is taken for granted. A charged battery sitting on a table contains energy. A lightning bolt contains energy. A nuclear reactor contains energy. Yet their usefulness differs enormously because of how controllably and rapidly that energy can be delivered. A charged battery sitting on a table contains energy. A lightning bolt contains energy. A nuclear reactor contains energy. Yet their usefulness differs enormously because of how controllably and rapidly that energy can be delivered. So, what we need, is to conquer our needs and utilize our energy. Thus, to accommodate that in the time needed, we need an idea of how fast it is able to suit our needs. This 'suit our needs' is the work we are trying to do. And when tared with time, we get the power.

The displacement is one thing. The time taken is another. Velocity tells us how aggressively one is trading time for position. Power then becomes the analogous trade for energy, the aggressiveness with which a system converts potential to output. And, so we know,

Which is why one would find the power of an electrical appliance written rather than the work done by it.

A relation between Force and displacement is thus natural, when we need to understand how much of our energy is actually being useful.

It is actually the theta in Fscos$\theta$ that links these two quantities together. It is the link between how connected our energy is with our goals. For nature does the energy bookkeeping, we as time-bound entities are naturally more interested in testing our bounds, and so arises the need to understand time and anything that changes with it :)

If we are being pedantic, there are again, conservative and non-conservative forces. While both do impact us, it does not work the way physics puts it in language. Honestly, putting the fact that non-conservative forces are path dependent, the distinction comes from force itself. A conservative force is one that conserves the same kind of energy to the same kind of energy. Electricity to electricity, mechanical energy to mechanical energy and so on. Take any example you want, all central forces are bound by the same brain. It is conserved in that sense and thus in a complete closed path,

Or equivalently,

That means the force can be derived from a potential function and the work done depends only on the endpoints. That's the rigorously physical part.

On the other hand, a non-conservative force is one that converts one form of energy to another, say mechanical to heat, sound, light and so on. The total energy remains conserved, but the energy becomes distributed among many microscopic degrees of freedom. Thus, it's actually the avatars of one entity influencing a seemingly independent avatar of the same entity.

Perhaps that changes your view on force as an existence?