Imagine a data center containing exabytes of data. How long does it take to access an arbitrary bit of that data?
We use clusters because computers cannot contain an infinite amount of memory, storage, or CPUs, because of physics. You see this same thing play out at smaller scales but it's more obvious at the macro scale. More addresses take logn time to sort out, but time to access is measured in radii, not gate depth.
In a world where clusters are rare, Knuth made decent approximations. In a world where clusters are not only de rigeur but hosted on multitenant hardware spread out over upwards of 100 miles, those approximations are bullshit and need to change.
But on the topic of hash tables, you can only reach 'O(1)' if you can avoid collisions. And to avoid collisions you need a key of length m, which grows as n grows. You cannot put 51 pigeons in 50 pigeonholes. So the key length of your hash keys is m >= logn, which means the time to compare keys is also logn, which means hash tables are never actually O(1) access or insert time. Actual access time for a hash table on non-imaginary hardware is √nlogn, not O(1).
If you consider that we have applications that are just a single hash table occupying the entire RAM of a single machine, then this is not picking nits. It's capacity planning.
I am not sure I am following this argument. You are not going to have more than 2^64 pigeons and pigeonholes on any system soon and I almost dare to say you will never ever get to 2^128. And for 64 or 128 bit keys comparisons and many other operations are for all practical purposes constant time. I guess you could argue that this is sweeping a factor of log(n) under the rug because of things like carry chains which could be faster for smaller bit sizes but I am not sure that this is really useful on common hardware, an addition will take one clock cycle independent of the operand values.
And that complexity theory already exists. Typical whiteboard engineering uses transdichotomous models to gloss over some polylogarithmic factors (as do much of the literature), but more accurate models exist.
The difference isn't usually super relevant when comparing multiple solutions all using the same model of computation though since the extra terms don't tend to bump one complexity class above another when switching models, and if you cared about actual runtime characteristics you wouldn't be relying on log factors in such a crude tool anyway.