The main reason is speed. Twinkle's optical adder is much faster than the question's proposed analog adder.
Twinkle's analog optical adder can operate at very high rates, in the gigahertz; much like we can transmit data at high speed over an optical link.
The arrangement proposed in the question, consisting of transistors (or transistor/resistor networks) in parallel, selectively drawing current, with the sum measured a common point, would only work at much lower speed, due to the distributed capacitance in the common node where the current converges. That distributed capacitance is bound to be proportional to the number of transistors connected, and would severely limit operating speed. We'd need to digitize (or at least sample) the result of local summations for centralized/hierarchical addition, and poof goes a lot of the simplicity/power-efficiency.