Isn't the conservation of energy just a trivial result which arrives due to the way kinetic energy and potential energy are defined?
The kinetic energy of a body of mass $m$ and velocity $v$ is defined to be $\frac{1}{2}mv^2$ and its potential energy due to some force $F$ is defined as a function of its position $r$ with respect to some reference position $r_0$ as $PE=-\int_{r_0}^rFdr$
So, the absolute total energy of a body can be calculated as: $$E=\frac{1}{2}mv^2-\int_{r_0}^rFdr$$
Now, this $E$ remains unchanged even if the position and velocity of the body changes if all the forces are conservative. But let's see how the change in $E$ is defined:
The change in $E$ is the change in $PE$ + the change in $KE$.
Now, the change in $KE$ is just equal to the work done.
$$\delta KE= \int_{r_1}^{r_2}Fdr......(1)$$ By the changing variable into $v$ $$=\int_{v_1}^{v_2}mvdv$$ $$=\frac{1}{2}m(v_2^2-v_1^2)$$
And, change in PE as the body moves from $r_1$ to $r_2$ is: $$\delta PE=-\int_{r_1}^{r_2}Fdr....(2)$$
Note that the integrals $(1)$ and $(2)$ just differ by sign. So, it's no surprise that the net change remains $0$. To evaluate the expression of change in $KE$, we change the variables of the integral to $v$. And, to get the expression for change in $PE$, we don't change the variable and we evaluate the negative of the same integral in terms of position. If change in $PE$ is just defined to be negative of change in $KE$, then isn't it trivial that the net energy remains unchanged?
Even I can attribute an unchanged quantity to a body. Suppose a body is acted upon by a force $F$ and I attribute this quantity to the body:
$$A=m\ln(v)-\int_{t_0}^t\frac{F}{v}dt$$ $t_0$ is any arbitrarily chosen time. This quantity is made up of two quantities: $B=m\ln(v)$ and $C=-\int_{t_0}^t\frac{F}{v}dt$.
The change in $C$ as the time changes from $t_1$ to $t_2$ is:
$$\delta C=-\int_{t_1}^{t_2}\frac{F}{v}dt$$
Suppose the velocity of the body at time $t_1$ is $v_1$ and at time $t_2$ is $v_2$. Now, the change in $B$ as the velocity of the body changes from $v_1$ to $v_2$ is:
$$\delta B=m(\ln(v_2)-\ln(v_1))$$ $$=\int_{v_1}^{v_2}\frac{mdv}{v}$$ $$=\int_{v_1}^{v_2}\frac{mdv}{vdt}dt$$ $$=\int_{t_1}^{t_2}\frac{F}{v}dt$$ $$=-\delta C$$
So, $\delta B+\delta C=0$. Hence, $\delta A=0$. So, $A$ is also an invariant quantity. Then, what's so special about conservation of energy if numerous invariant quantities like $A$ can be attributed to a body?
In fact, defining $PE$ requires the force to be conservative because there can be infinitely many paths joining point $r_0$ to $r$ and we require $PE$ to be independent of path followed. But for defining the quantity $C$ there is no such restriction on the nature of force because time can only flow along a unique path from $t_0$ to $t$. $PE$ relates every point in space to a number whereas $C$ relates every time instant to a number.