I mean, you're not wrong. A meteor striking the Earth, making the conditions in an ecosystem inhospitable to life without necessarily introducing a cycle of degradation is consistent with your commebt. But that's not mutually exclusive with humans introducing a species that later becomes invasive, ultimately resulting in fundamental alterations to the ecosystem.

The weak die off, but the strong may adapt and move on, repeating the cycle in other areas.

See, the thing is, particularly in areas prone to high summer heat and direct exposure to the sun, when the cows overgraze, this not only kills off the plants, but when the plants die back, there is nothing to shade the soil. The soil then bakes in the sun, often times reaching temps above surface air temperatures. The high heat bakes other plant roots as well as increases evaporation of nearby surface water as well as further drying out the soil. So the water hole eventually dries, along with much of the remaining vegetation.

But the those who adapted move on to another watering hole, restarting the process.

People don't realize how much of a driver of desertification overgrazing is. It wasn't historically an issue when bison and other large herbivores were more prevalent, but humans wiped them out, along with their predators. With feral cows, there's nothing really forcing seasonal herd migrations, so the vegetation never has a chance to recuperate. This is particularly notable in areas with sparse water access to drink from - they will stay near the water, overgrazing the vegetation until it no longer grows back.