This is always a point of frustration for me. Under the normal big-O model, hashtables aren't, and can't be O(1) lookup, even for the mythic perfect hash function! You can only get the O(1) figure by breaking the big-O model and bolting on some in-practice assumptions[1] that are used nowhere else in discussion of asymptotic complexity.

Specifically, as you resize the table, you need a function with a bigger output space to give you more places to store the item. To have a bigger output space, you unavoidably have to do more computations. If you go from a function with n possible outputs to one with 2n possible outputs, as n goes to infinity, you eventually have to use a function with more steps.

[1] elaborated on in this earlier discussion: https://news.ycombinator.com/item?id=9807739

Specifically this comment about the extra assumptions: https://news.ycombinator.com/item?id=9813524

O(1) lookup is bullshit that ignores the memory hierarchy.