FPGA doesn't seem to work the way I imagined
It is a giant array of switches, yes.

Specifically, an FPGA cell will usually have one state element (D-flop) with a lookup table (LUT) on the input. The LUT is programmed to give a particular output for each possible combination of inputs.

Additional switches connect the cells to a routing network of wires. There are usually also a number of specific-purpose blocks for doing common operations like additions and multiplications, small memory blocks of (say) 1kb each, and high-speed transceivers for doing things like Ethernet or PCIe.

It really isn't like a microprocessor and does deliver large amounts of single-cycle logic in parallel. However for integer non-parallelisable tasks a regular CPU may have higher throughput, or for the very specific workload they are designed for GPUs are faster.

FPGAs give you low-level access to signals with low, fixed, latency. That's their real value.