FPGA-specific soft cores like VexRiscv and NaxRiscv are immensely useful for anything involving state machine logic or glue code that you do not want to implement in-fabric.
Peripherals like on-chip MMCMs/PLLs, on-board I2C and SPI peripherals, etc. with complicated initialization routines or communication flows or sequencing are very easily handled in a soft CPU.
Soft CPUs can also be used like high-powered programmable in-circuit logic analyzers: without rebuilding a potentially massive FPGA bitstream, you can probe/observe/inspect, inject/alter any signals or buses you pipe to the CPU. VexRiscv is far more pleasant to use than any vendor ILA IP.
Soft CPUs also normally utilize FPGA LUTRAM/BRAM resources, enabling whatever program to run with hard real-time latency consistency.