It's possible that if FPGAs continue to improve as they are and catch up with ASICs in terms of density and price then reconfigurable HW may become a possibility.

At the moment, most of those task would be done on ASIC, so yes we might see those tasks done on FPGA.

There wouldn't be advantage in performance generally, only in that you could have true HW updates.

It is something I've been thinking about in that you could theoretically have a processor optimized for the game. So you could download HW on the fly (pre built) and flash your machines FPGA.

There is a trend on integrating processor, FPGA, memory and high bandwidth pipes between them on a single package. Database heavy applications are among the first adopting these architectures, it can be that others will follow.