There can be more than one reason.
Yes, but this is not really one of them. Yes, captive breeding is the
only thing keeping the species afloat. Without captive breeding, they would be completely gone from this world. They breed very, very readily, which is one reason why they are popular among scientific studies. There is no need to harvest them from the wild because they reproduce with very little prompting. If you can get hundreds of axolotls and multiple generations from a single pair, why would you repeatedly take them from the wild?
Axolotls came from a series of lakes called the
Canals of Xochimilco. The lakes have a number of problems. They are polluted, drying up, and unnatural predators are being introduced. Before that, there were thousands of axolotls per square mile. Once the lake started dying and the Mexican government took a stance that they wouldn't be restoring it, the population quickly started to die out. By 2014, there were no wild axolotls in what was left of Xochimilco. If the lake was okay, the axolotls would be as well. Sadly, that is not the case. That is the reason why they are teetering on the edge,
not their use in research.