I’d love to see that common thought validated because in practice I’ve seen it to not be true at all.
There are lots of cases where the complexity effects of the algorithm are swamped by cache effects. In fact basic foundational assumptions about complexity analysis are dangerously untrue on modern systems.
In my experience in either high throughput or low latency systems algorithmic complexity is never the issue. It’s always cache coherence, CPU prefectching/prediction, lock contention or over copying of data.