Thanks for the comments Ralf!
You cannot switch the default behavior, that will break backwards compatibility.
The default `kind=None` have no effect on input/output behavior of the function. The only changes a user will see are in terms of speed and memory usage. `unique` will select this new algorithm `"table"` only if it is available (integral array, no axis specified, return_index and return_inverse set to False) and the required memory allocation is not too big (which is arbitrarily defined as six times the allocation of the input array - similar to what the sorting method use). Using `kind="table"` won't affect the input/output either, but it is only available for certain arrays (somewhat similar to the usage of `assume_unique` for `np.isin`). Does this sound fine to you?
Regarding the name, `'table'` is an implementation detail. The end user should not have to care what the data structure is that is used. I suggest to use something like "unsorted" and just explain it as the ordering of results being undefined, which can give significant performance benefits.
The names `'table'` and `'sort'` were selected for consistency as these names were recently put in place for `np.isin` and `np.in1d`, and the analogous methods used for `unique` are conceptually similar. I have no particular attachment to either name though. Thanks again! Miles