> Even when something isn't a galactic algorithm "how well it maps to being done efficiently in real hardware with hardware sized data sizes" is more and more often the important bit over "slightly better bounds at infinity"

You're just repeating the same claim. Why is that more and more often then important bit? Why is it more important now? Why are these factors not captured in complexity analysis?

For instance, some complexity analysis assumes random access memory of arbitrary size, but memory above a certain size is better modelled with logarithmic access time. But this too can be captured in complexity analysis, so it's not really evidence of any divergence.

And then you have cache-oblivious data structures that scale uniformly across all cache sizes, which is a product of complexity analysis.

So I'm asking for what exactly is being meant with a justification of why you think this matters now more than it did before.

A contributing factor is how complex/smart the current hardware is. It can have cache line size, different forms of hardware/software prefetching, different ports for different ops, memory latency, simd extensions. These leave many opportunities for algorithms to be optimized over. There is also the issue of real life scenarios not matching with asymptotic ones (due to e.g., size of input), which when coupled with previous factors, leads to even more potential optimization schemes. Obligatory reference: https://agner.org/optimize/

Complexity analysis typically assumes an ideal Von Neumann machine. Systems programming embraces the discontinuities in registers, L1, L2, L3, ILP, branch prediction, and so on. (Maybe there's a good pun to be had that complexity analysis stays as far away from computer complexity as possible.) The simple model is essential, as it's the only way to create a body of proofs that will last. What's increasingly hard, though, is that there are oodles of papers, of the sort demonstrating that one algorithm or data structure is better than another, yada yada, and there's usually some benchmarking in each, and that kind of empirical demonstration is now far less than useful unless the paper's authors are good systems programmers and have given up on improvements.