Anaerobic vs Aerobic training should not be considered exclusive of one another. They are complementary pieces meant to maximize swimming efficiency over a given race. Specificity of training for the purpose of racing is the efficiency of timely, useful work toward achieving your performance goals.
Anaerobic Limits to Training and Racing
Anaerobic glycolysis does not require oxygen to generate energy. So while less energy is produced, it is available faster, making it particularly useful for sustained maximum efforts lasting ~:40 seconds or less. One of the initial byproducts of these max efforts is lactate. Or half of the whole that creates lactic acid. Once thought the scourge of performance.
But we now know that lactate is fuel for the mind, heart, and body. Capable of being transported in a multitude of ways, including waste as lactic acid. The presence of blood lactate is correlation but not causation for fatigue.
Instead during workout we can use lactate markers to identify and challenge training for the purposes of tolerating the negative effects of the associated metabolites. The maximal lactate steady state (MLSS), onset of blood lactate accumulation (OBLA) and the Lactate Threshold (LT) provide benchmarks. Manage your blood lactate levels within acceptable limits and all is well. Brazenly move past them and an exponential pain is headed your way.
Aerobic Training Benefits Every Athlete
Aerobic glycolysis uses oxygen to produce more energy over a sustained period of time, but does not reach its maximum potential til ~2 minutes into a race. Think of a 200 swimmer who 'goes down' to the 100 - typically they will 'back-half' their race. So the key is balancing availability over time.
Like anaerobic training is inevitably linked to lactate, aerobic is synonymous with vo2 max. But unlike blood lactate testing, measuring vo2 max requires a commitment to a graduated step test that starts slowly so as to introduce aerobic pathways. Then finishes when the athlete collapses or hits widely accepted minimum benchmarks including a blood lactate of 8 mmol.
Another benchmark is the respiratory exchange rate - ratio of o2/co2 at the mouth. For a swimmer who 'holds' their breath underwater this can be extremely tricky. But athletes always find a way - whether it be a second wind during a race/training or rapid deep breaths before it. Even the heavy breathing between repeats or gasping for air after the race allows the blood flow from the metabolic waste from anaerobic training to create an aerobic training effect - oxygen debt/EPOC.
Anaerobic vs Aerobic should be 'With'
There is always a way. As alluded to earlier, a race is the sum of its parts. Training should reflect race strategy and schedule.
To attempt a 'phelpsian' schedule, any athlete should have a serious aerobic 'base' to their season. To race the 50, athletes should be primed to pounce like a lion, not race multiple 50's. And to have a finishing kick to the 200, a swimmer must challenge their aerobic and anaerobic abilities. Periodize sets, workouts, and weeks to effectively manage physiological efficiency.