There is never a physical justification for a basis change. As you should know changing bases does not change any of the actual physics, it is always for mathematical reasons that basis changes are performed, for example making calculations easier or some things easier to see., there is no physical justification for the above basis change.
Besides, justification is in the result. And in the case of the simpler one in post 32, to test your level of knowledge on the subject as it was a complete give-away.
Huh? Here is someone:Also, show that someone else (rather than you) elected to stick the Schwarzschild radius into the Minkowski metric.
So you might as well ask yourself the same questions, maybe you'd see how silly they are.