Is it more correct or preferable to write $$ x = \begin{cases} a, & b; \\ c, & d;~\text{and} \\ e, & f. \end{cases} $$ than simply $$ x = \begin{cases} a, & b, \\ c, & d, \\ e, & f. \end{cases}? $$
It seems to me that the former is more grammatical (especially when one considers writing these conditions without using symbols), but is more cumbersome than the latter.
Similar question can be found here.
It is exceptionally common to omit the conjunction in lists in notation. Example: "Let $a,b,x,y \in \Bbb{R}$."
One justification for the omission in your example is that you are not writing a list. You are collecting a set of partial functions with (required) disjoint domains and one does not normally put a conjunction into a complete listing of the elements of a set. Example: "Let $A = \{1,2,3\}$."
Finally, the placement of the "and" draws additional attention to that line of the multiple cases. Unless there is something special about that line, there is no reason to draw the extra attention.