Why use two separate tables in cuckoo hashing? I've been reading a number of papers on cuckoo hashing, including several that generalize it by talking about cuckoo hashing with multiple tables, cuckoo hashing with a stash, the (multi)graph-theoretic properties of the cuckoo graph, etc. However, I have not seen any papers discuss why cuckoo hashing typically separates out the slots into distinct tables rather than having one larger table with multiple hash functions indexing into it (though I did come across a set of lecture notes aimed at undergraduates where this simplification is used).

Is there any particular reason for this?
One reason is that when there is only one set of slots, there will be some keys such that $h_1(k) = h_2(k)$.