Yes and no. If you took the same processor design and synthesized it for an FPGA and had a custom ASIC made, the latter should run a lot faster — at least an order of magnitude. So why use FPGAs? You can easily build a system-on-chip that integrates a processor and lots of other custom stuff, like glue logic to hook up other devices, along with DSP blocks and clock circuitry. You can do that in quantity 1 if you like (a 1 off ASIC would cost a lot more...) and you can also modify and update the design just by replacing a configuration file in flash.
Cost and ability to reconfigure/update aside, FPGAs allow you to implement application-specific stuff in hardware, such as signal processing, and that can run a lot faster than when implemented in software, given FPGAs are inherently parallel. Maybe a couple of orders of magnitude? A great deal faster anyway.
RF switching is handled by the LMS7002M, with I think the exception the loopback function. The GPIO is connected to the FPGA and custom logic could be implemented there to control/interface with this.