To prevent collisions, hash tables with open addressing use a methodology to chain the contents. Why can't we use another hash table allocated to each slot of the primary hash table?
The method you propose is, as far as I know, the historically first one for "perfect" hashing in linear space. In perfect hashing, lookup takes $O(1)$ time in the worst-case. (Recall that in most simple hash tables, lookup takes $O(1)$ time only in expectation.)
The idea is to use chaining (rather than open addressing), but make each chain a hash table of size $\Omega(m^2)$ where $m$ is the number of items in the bucket.
This is sometimes called "FKS", after the initials of the inventors. Here are some freely available resources:
- "Universal and Perfect Hashing" by Avrim Blum
- "Storing a Sparse Table with $O(1)$ Worst Case Access Time" by Fredman et al.
- "Dynamic perfect hashing" (Wikipedia) supports dynamic insertion and deletion with expected amortized $O(1)$ time, in addition to (like other perfect hashing algorithms) $O(1)$ worst-case lookup time.
The short answer is that this is, more or less, equivalent to having one hash table. Let's say you're hashing $n$ items into $m$ slots, and each slot has its own hash table of size $c$. You propose first hashing into one of the $m$ slots using some function $h$, then hashing again into one of the $c$ slots using some function $g$. This is more or less equivalent to hashing to any of the $cm$ slots initially, with a new hash function that combines your initial two hash functions. In other words, instead of taking $h(x)$ for which of the $m$ slots to hash it to and then $g(x)$ to find the appropriate slot in the subtable, you can take $f(x) = h(x)m + g(x)$ and get the same answer with a new hash function $f$.
Something else to consider is what you do if there are collisions in the second hash. You need...some sort of methodology to chain the contents! So you're back where you started with linear probing/chaining/etc, and all you've done is increase your hash table size from $m$ to $cm$.