Why is fermentation so important under anaerobic conditions?

The first step of either anaerobic or aerobic respiration is glycolysis. It takes place in the cytoplasm. Glycolysis breaks down a molecule of glucose to produce two molecules of pyruvate (pyruvic acid), two molecules of NADH, and a net gain of two molecules of ATP. If oxygen is present, the pyruvate will enter the mitochondria where aerobic respiration will take place. In the absence of oxygen, the two pyruvate molecules will undergo either lactic acid fermentation or alcoholic fermentation, depending on the orgainism.
The purpose of fermentation is to clear the pyruvate and to oxidize ##”NADH”## back into ##”NAD”^+##, which is used again in glycolysis with another glucose molecule. Without fermentation, glyolysis will eventually stop when all of the ##”NAD”^+## is converted into ##”NADH”##. Therefore, no net gain of 2ATP will be produced, and the cell or organism will die,
In lactic acid fermentation, the pyruvate is converted into lactic acid. In alcoholic fermentation, the pyruvate is converted into carbon dioxide gas and ethyl alcohol (ethanol).
The overall reaction of glycolysis is:
##”glucose”## + ##”2ADP”## + ##”2NAD”^+## + ##”2P”_i## ##rarr## ##”2 pyruvate”## + ##”2ATP”## + ##”2NADH”##
The ##”2ATP”## represents a net gain of ATP, which is able to be used by the cell to do work. Notice that fermentation does not produce any more ATP. So glycolysis followed by fermentation results in a net gain of ##”2ATP”## for every glucose molecule,
The overall reaction of lactic acid fermentation is:
##”2 pyruvate”## +##”2NADH”## ##rarr## ##”2NAD”^+## + ##”2 lactic acid“##
The ##”2NAD”^+## are free to be used with another glucose molecule in glycolysis.
The overal reaction of alcoholic fermentation is:
##”2 pyruvate”## +##”2NADH”## ##rarr## ##”2NAD”^+## + ##”2CO”_2## + ##”2 ethanol”##
Like lactic acid fermentation, the ##”2NAD”^+## are free to be used with another glucose molecule in glycolysis.