There are species that thrive in many ecosystems, from the Brahman types in the tropics to the long haired Highland cattle of Scotland. Yaks are in the family, they are living in rather arid conditions in central Asia. The longhorns from Spain can go wild in western US deserts. Desert is a relative term, cattle don't go to the extremes as well as goats and camels, but they can live in arid areas. The key thing is to much more closely control numbers.
People have to be out there, watching.
Wiping out predators, then just throwing the animals out there and not watching the impact, is irresponsible, but that doesn't mean that one can't be responsible. Shipping animals off the land to feed people in far away cities is also unsustainable, it takes a lot of energy, and it takes nutrients off the land, same as any crop. I don't condone what is being done, but I don't think that sweeping condemnation of cattle is the answer either. This is only the tip of the tip of the iceberg. They are low-efficiency consumption machines.