Polarimetric phased arrays can equip radar systems with enhanced measuring abilities but also incur high costs. This study introduces a low-cost architecture and its applications in polarimetric phased-array antennas to perform multiple tasks with an acceptable tradeoff. In this architecture, the ports of each dual-polarized element are connected to a shared channel using an element-level-controlled polarization switch. Thus, the number of components is reduced by almost half. By shifting the switches, elements can be formed into either a full array with single polarization or interleaved thinned arrays with dual polarization. For the latter, a thinning method is presented based on central symmetry constraints and sidelobe optimization. Simulation experiments on an $8\times 8$ planar array demonstrated that the proposed method can effectively obtain highly matched copolar beams with well-controlled sidelobes.