The decomposition into electric and magnetic fields is valid in a specific reference frame, those fields mix under Lorentz transformations. Based on that, you may expect that this separation will be more useful in the non-relativistic (low energy) limit. There is also the historical fact: Maxwell equations were written down before special relativity was discovered. Since we still, by and large, make the odd choice of teaching things in historical (rather than logical) order, you've probably seen Maxwell equations in components before seeing them in their more compact and symmetric form.
But, for fields relevant only in very high energies (the electroweak gauge bosons), which were also discovered after SR, the relativistic form of the equations is the default. You can certainly write things in components, but this is not a very useful notation.
There are some exceptions, some corners in high energy physics where this decomposition can give you some intuition. For example if you look at the QFT text by Peskin and Schroeder you'd find some intuitive picture on why the $\beta$ function of non-Abelian gauge theories is negative. This picture is not gauge invariant, but it relies on some "magnetic" as opposed to "electric" effects. But these exceptions are rare and not always all that useful.