Could you please elaborate on the rationale behind the utilization of MUX, or multiplexer, in Field-Programmable Gate Arrays (FPGAs)? I'm curious to understand how it contributes to the flexibility, efficiency, or functionality of these devices. Are there specific advantages MUX offers that make it a preferred choice for FPGA design? Additionally, how does the implementation of MUXes within an FPGA impact the overall architecture and performance of the system?