CO₂ from carbonate-based capture solutions requires a substantial energy input. Replacing this step with (bi)carbonate electrolysis has been commonly proposed as an efficient alternative that coproduces CO/syngas. Here, we assess the feasibility of directly integrating air contactors with (bi)carbonate electrolyzers by leveraging process, multiphysics, microkinetic, and technoeconomic models. We show that the copresence of CO₃^2- with HCO₃^- in the contactor effluent greatly diminishes the electrolyzer performance and eventually results in a reduced CO₂ capture fraction to ≤1%. Additionally, we estimate suitable effluents for (bi)carbonate electrolysis to require 5-14 times larger contactors than conventionally needed contactors, leading to unfavorable process economics. Notably, we show that the regeneration of the capture solvent inside (bi)carbonate electrolyzers is insufficient for CO₂ recapture. Thus, we suggest process modifications that would allow this route to be operationally feasible. Overall, this work sheds light on the practical operation of integrated direct air capture with (bi)carbonate electrolysis.