Definition of RLC resonance frequency
For example, the RL-C series-parallel circuit

I'm assuming here you mean a series connection of a resistor and inductor where that series pair is in parallel with a capacitor. The impedance of that circuit can be found to be: -
$$\dfrac{\frac{1}{LC}\cdot\left(R + j\omega L\right)}{\frac{1}{LC} - \omega^2 + j\omega \cdot\frac{R}{L}}$$
Note the \$\frac{1}{LC}\$ terms.
The square root of that term (in these particular types of 2nd order circuits) has a special name. It is called the natural resonant frequency (or pole frequency) and is given the symbol \$\omega_N\$ (or \$\omega_0\$).
Hence, \$\omega_N^2=\frac{1}{LC}\$
That's all it means when we talk about \$\frac{1}{\sqrt{LC}}\$. We find it commonly occurring in these types of equations and, it has enough relevance to be given a meaningful name.
For differing configurations of R, C and L, it can have different connotations but, nevertheless, we still link the name directly with \$\frac{1}{\sqrt{LC}}\$.
In a particular circuit, if we are interested in &quot;other things&quot; (such as maximum impedance or, the frequency at which the impedance is purely resistive) then we have to be specific about what we are talking about. Therefore, it's naïve to talk about a term such as &quot;resonant frequency&quot; with no further definition of what we actually mean.

Definition of RLC resonance frequency


My question is why is it defined this way?

We shouldn't attach a specific meaning to the term &quot;resonance frequency&quot; (or resonant frequency). However, the term &quot;natural resonant frequency&quot; (aka pole frequency) is defined as \$\frac{1}{\sqrt{LC}}\$.