That is not how we keep cattle in the United States. In the US about 82% of grazing land is rangeland, which continues to support the natural ecosystems (prairies, shrublands, steppes, etc).

In places like Ireland, where cows have existed for 6000 years, they're also part of the ecology by any meaningful metric. There are a lot of more recently arrived species considered native! Mice, hedgehogs, rabbits, and red deer all came later.