Aren't most DEs not solvable analytically? i.e. only a tiny subset are neatly solvable - like precisely manufactured puzzles. In general, for any real problem you encounter "in the wild", numerical methods are the only way to find solutions (which are approximate).
DE theory is still useful for designing frameworks within which numerical methods can operate.
Yeah, I think "mettle" here is like a sword and shield and the ability to use them (read and understand scientific literature, and able to do so, self-directed, for years).
But whether a person does use them, and for what, is entirely due to the person themselves.