Naive Merging

The obvious approach: pick one child's set as the base, then insert all elements from other children's sets one by one. For each child set of size $k$, you do $k$ insertions. If you have sets of sizes $s_1, s_2,., s_c$, you pay $s_1 + s_2 +. + s_c$ operations per node.

This seems fine per node, but across the whole tree it breaks down. The total cost depends on which set you choose as the base. Choose poorly and you hit quadratic time.