Partitioning the energy of a signal between its components
Say you decompose the signal $x(t)$ into two components: $$s(t) = x(t) + y(t).$$ As you say, there are myriad ways to do this. The energy of $s(t)$ is $$E_s = \int_{-\infty}^\infty s^2(t) dt.$$
If we calculate it using the decomposition, we obtain:
\begin{align}E_s &amp;= \int_{-\infty}^\infty (x(t) + y(t))^2(t) dt \\
                 &amp;= \int_{-\infty}^\infty x^2(t) dt + \int_{-\infty}^\infty y^2(t) dt + 2\int_{-\infty}^\infty x(t)y(t) dt
\end{align}
Clearly, if you require that $E_s = \int_{-\infty}^\infty x^2(t) dt + \int_{-\infty}^\infty y^2(t) dt$, then it is necessary that $$\int_{-\infty}^\infty x(t)y(t) dt = 0$$ or, in other words, $x(t)$ and $y(t)$ must be orthogonal.
By the way, I have never seen it claimed that all existing decompositions have the energy-conserving property you are looking for, not even in the context of physics rather than engineering.