I see where you're going with this - it seems potentially contradictory. I should probably clarify that it depends on construction and fingerboard material.
Not too stiff because an overly stiff neck and phenolic fingerboard creates a very brittle sounding instrument. I've played early to mid nineties Status Empathy and Modulus Quantum basses with this quality. For extra context, other bass makers like Ken Smith aim for a neck that is just stiff enough because it introduces some warmth into the lower mid range and tames the highs a little.
Overdesigned means designed far beyond what is needed to resist string tension. That could mean the number of layers of weave used (typically more than three layers), the orientation of the weave in selected locations and the choice of unecessariy thick fingerboard material.
Purely based on observation alone, in the late 70's necks seemed over designed. Super rigid but also very easy to fret dress and achieve incredibly low action. The problems with aftermarket Modulus necks in the early to mid eighties were apparently due to Geoff Gould delegating the mixing of phenolic resin while he was off setting up Modulus operations and the person responsible not paying sufficient attention. It was why Alembic ditched graphite necks as an option.
However, I've played early 90's Modulus basses with floppy necks too - just had a 92 Quantum 5 pass through my hands for set up and restoration with a neck that wasn't stiff enough to resist string tension and there was no way to set the bass up with reasonable action. I've also owned a 94 with a neck that was brittle and a 96 with a banana neck. And a 96 Sonic Hammer that was just fabulous in action and sound. QC seems a little inconsistent to say the least. Ironically the Modulus basses with flexible necks sounded great - really growly and warm.