It's certain it wouldn't be able to reach the same frequencies and would eat up more resources.
Since you pretty much have it all figured out, I can't see what it would bring to the table.
The statement is true, but it completely misses the point, I see very very few instances where a digital PID controller working at such extreme frequencies can be actually usefull in real life (other than as a d**k measuring context), so the frequency advantage while technically true is not applicable
As for the resources, modern FPGA’s are so large that using a tiny soft core or two is not that much of an issue
EDIT: on the resources side, calling the processing unit a soft core is also very generous, as for most type of non adaptive controllers including Not only PIDs but much more advanced stuff you can really get by without even having loops and jumps, as you are executing mostly just a series of math operations chained together, this also simplified the control unit design greatly (that means you will have to write your own assembler/compiler though as I think adapting LLVM to such a strange architecture would be quite strange