That is very clearly NOT how harvesting herbs works. Here is the real mechanism:

Each crop that has a random yield (herb, allotment, hops) has 3 "lives." Every time you pick one, there is a chance for the plant to lose a life. When the plant loses all 3, it is removed. The chance to lose a life is determined by what kind of crop you are farming (herbs have a much higher chance than allotment and hops), your farming level (only very slightly), and any bonuses you currently have. This includes amulet of nature, magic secateurs, and farming cape. These 3 items do NOT increase the minimum yield of the plant; they only make it less likely to die.

Compost, on top of reducing disease chance, significantly reduces the chance to remove a life, increasing yield. In addition, it gives the plant 4 lives minimum. Supercompost has the same effects, but better, also giving the plant 5 lives.

Therefore, while you can't see the effects of the farming cape on a single crop, it does give you 5% higher yield statistically in the long run.