According to hyperphysics.edu, and my general knowledge, anaerobic respiration occurs in the cytoplasm. ("Anaerobic respiration (both glycolysis and fermentation) takes place in the fluid portion of the cytoplasm whereas the bulk of the energy yield of aerobic respiration takes place in the mitochondria".) Is there a biochemical advantage to this, or do eukaryotic cells simply lack specialized anaerobic respiratory organelles? I could understand this; few cells use this form of respiration besides muscle cells. But even in muscle cells, it occurs in the cytoplasm. Why? Is it simply taking advantage of fortuitous chemical circumstances, or was it evolutionarily desirable to respire anaerobically in the cytoplasm and aerobically in the mitochondria? I am aware, also, of the endosymbiotic theory of mitochondria.
The problems here would seem to be (1) a misconception of the biochemistry of anaerobic respiration — strictly anaerobic glycolysis or fermentation (see this Wikipedia article for explanation of the term), (2) not considering the bacteria in which these processes evolved rather than eukaryotic cells, and (3) a failure to regard the lack of organelles as the default situation.
The majority of the reactions of anaerobic fermentation constitute glycolysis, and glycolysis was probably the way in which most bacteria obtained energy before the great oxygenation occurred. The ATP is generated ‘at the substrate level’ — i.e. in the actual reactions — and there is no biochemical reason to think the pathway would need to evolve anywhere other than the bacterial cytoplasm, where the ATP would be available to reactions that need it and the various metabolites could feed in or out to other pathways. The product (lactate in mammals, but also ethanol etc. in bacteria) could easily diffuse out of the cell.
Why on earth should one imagine “specialized anaerobic respiratory organelles”? They are just not required and, for example, would impose an energetic cost for shuttling of metabolites in and out of them, as is the case for mitochondria.
The pertinent biochemical question is not, I think, “Why do eukaryotic cells lack anaerobic respiratory organelles?”, but “Why do the cells need an organelle — the mitochondrion — for aerobic respiration?”. There is a specific answer to this, which is not some vague concept of tidy subdivision of the cell.
This specific answer is, in brief, that aerobic respiration requires a compartmentalized system separated by a membrane so that a pH and charge gradient can be established, to be used subsequently to generate ATP. In Gram-negative bacteria it is the double membrane that provides this; and in eukaryotes it is the successor to the captured bacterium — the mitochondrion.
So there is a good reason for eukaryotic aerobic metabolism to require an organelle, and no reason that I can see for anaerobic metabolism to do so.