Hi Tom,
Yes, chronic lack of K ultimately slows growth due to the wide range of activities and processes in which it is involved in, - not the least of which is Photosynthesis and Amino acid/Protein synthesis. In fact, farmers and gardeners often dose extra K which promotes the nutritional value of their crop yields. In fact any crop that is a sugar based product needs lots of K to synthesize and even to store the carbohydrates. Crops such as Sugar cane, sugar beets, sweet potato and so forth are optimized with lots of K. K is also essential for root development and function so that tubular crops are also optimized via massive K dosages. K is used in the formation, translocation and storage of the carbohydrates so that grain crops such as wheat, corn, and barley also have higher yields when fed high K dosages. K is also essential in the formation of oils so that oil crops such as soybean, peanuts and flax produce higher yields with more K. K is involved in so many processes that the optimization effects are wide ranging.
While algae are plants too, and while they do use K, their blooms are not induced by high available K concentrations.
Too much K never hurts and does not drive the downstream effects to cause shortages that the other macros do. In fact, the concentration of K within the plant is reported to be much higher than is actually necessary. This might be considered a form of long term storage (what Barr calls "Luxury uptake").
A brief history of K: Hundreds of years ago wood and other organic matter was burned in pots in the process of fabricating soap. This burnt residue, or, ash was called unsurprisingly, "Pot Ashes" and was basically a cocktail of various Potassium salts. After rinsing, the ashes were dried and later combined with animal fat to produce the soap. Pot ashes, later became known as Potash and is therefore associated with K - in effect Pot_ash_ium or Potassium. Now, any salt of K is referred to as a type of Potash, so for example the expression "Potash of Nitrate" is simply Potassium Nitrate (KNO3) and Potash of Sulfate is Potassium Sulfate (K2SO4).
Cheers,