No, that is not the reason why it doesnt work.
Ive been watching a lets play in the 1.16 where no farmers are needed and it still works, its literally the same build that the one in the pic.
Ive done what you suggest anway, but it still isnt woeking.
Also ive build other 2 designs and they also are not working.
EDIT: I found that the gamerule for mob griefing must be true, still some of the tutorials I followed still dont work with the rule on