FPGA's have the advantage that the circuit architecture can be designed specifically for the algorithm but as far as I know they have much lower gate density and clock speeds compared to top of the line GPU's.
In the case of bitcoin mining as far as I know GPU's passed the hat directly to ASIC's. I never heard that FPGA's were competitive for that.
Additionally, GPUs are optimized for throughput. CPUs are optimized for latency, I haven't seen the benchmarks but I'd blindly bet that a modern CPU could get lower latency on this problem than a modern GPU.
The blog post here solved the entire problem in just 3 clock cycles. I don't know how the numbers come back on a GPU or CPU, but the vast majority of the optimizations here are completely impossible on a standard instruction set, and would instead require doing dozens to hundreds of clock cycles. Going from 65 MHz to 5 GHz isn't going to make up for all the shortcuts you lose out on.
They were, before the ASICs came. CPU -> GPU -> FPGA -> ASIC. A classic story of specialization.
FPGAs are a lot better than GPUs from the perspective of energy efficiency, but the FPGAs themselves are very expensive to purchase, and are a lot more specialized than GPUs. ASICs showed up before FGPAs ever really took off, and even if ASICs hadn't showed up it's not clear that FGPAs would have been superior on a total-cost basis to GPUs except in niche circumstances.
What do you mean by "more specialized" ? FPGA's can implement any logic circuit whereas GPU's are optimized for highly parallel arithmetic computations. I don't understand how that makes FPGA's "more specialized". It seems like they are in fact more general.