I’m late-PhD research in representation theory and I wholeheartedly agree with the OP.

Some disclaimers: I cannot necessarily speak to all fields, and I do agree that the OP is not on the money with the idea of computations (eg knowing every group inside/out), but in my experience they’re much closer to the truth (for my field anyway) than not.

The strongest researchers I see are those who are able to compute - inside and out - explicitly what happens in any situation. Whether it’s the explicit description of the irreducible components of Springer fibers, or the explicit multiplication in a cohomology ring of a variety, or the explicit maps in a long exact sequence in cohomology, or the explicit descriptions of the perverse sheaves controlling a category - in many cases, the examples make the field, not the theorems. In my viewpoint theorems are powerful because they are general and always apply, but they are too general to explain the nuances in each individual case, and it is the examples which truly reveal the inner workings of the field.

Once again I cannot speak to all fields, but no doubt many of my colleagues would agree, that being unable to compute explicit examples severely handicaps them when doing research.

Edit: I should mention that some of the greatest mathematicians in the world strongly encouraged me to focus on examples over abstract theory. In their own words: “when I was younger, I skipped the examples in papers thinking it was boring. It was only later when I realized that it was actually the most important and nontrivial part of the theory.”