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Estimating the size of the union of a stream of sets S₁, S₂, …, S_M where each set is a subset of a known universe Ω is a fundamental problem in data streaming. This problem naturally generalizes the well-studied 𝖥₀ estimation problem in the streaming literature, where each set contains a single element from the universe. We consider the general case when the sets S_i can be succinctly represented and allow efficient membership, cardinality, and sampling queries (called a Delphic family of sets). A notable example in this framework is the Klee’s Measure Problem (KMP), where every set S_i is an axis-parallel rectangle in d-dimensional spaces (Ω = [Δ]^d where [Δ] := {1, … ,Δ} and Δ ∈ ℕ). Recently, Meel, Chakraborty, and Vinodchandran (PODS-21, PODS-22) designed a streaming algorithm for (ε,δ)-estimation of the size of the union of set streams over Delphic family with space and update time complexity O((log³|Ω|)/ε² ⋅ log 1/δ) and Õ((log⁴|Ω|)/ε² ⋅ log 1/(δ)), respectively. This work presents a new, sampling-based algorithm for estimating the size of the union of Delphic sets that has space and update time complexity Õ((log²|Ω|)/ε² ⋅ log 1/(δ)). This improves the space complexity bound by a log|Ω| factor and update time complexity bound by a log² |Ω| factor. A critical question is whether quadratic dependence of log|Ω| on space and update time complexities is necessary. Specifically, can we design a streaming algorithm for estimating the size of the union of sets over Delphic family with space and complexity linear in log|Ω| and update time poly(log|Ω|)? While this appears technically challenging, we show that establishing a lower bound of ω(log|Ω|) with poly(log|Ω|) update time is beyond the reach of current techniques. Specifically, we show that under certain hard-to-prove computational complexity hypothesis, there is a streaming algorithm for the problem with optimal space complexity O(log|Ω|) and update time poly(log(|Ω|)). Thus, establishing a space lower bound of ω(log|Ω|) will lead to break-through complexity class separation results.