I can't speak for what the OP meant, but at least out West cattle fill a critical role in the wilderness ecosystem vacated by bison. If you remove the cattle, you would need to find a suitable replacement with similar grazing patterns.

As a well known example, pronghorn antelope benefit significantly from coexisting with cattle/bison populations, due to reduced predation and increased food supply (they have complementary feeding patterns). Grazers create ideal habitat for pronghorn, so pronghorn populations tend to track grazer populations. These days, that is cattle.

I am talking about out west. I hadn't thought of the bison angle, but thats a good point. (I'm a geek, not a rancher, so my knowledge on these things is anecdotal from listening to the old timers)

I thought we were talking about forests, not grasslands.

One of the primary benefits is that cattle help clear underbrush, which therfor produces more productive stands of timber. If kept in one area too long though they will begine to damage trees, so proper rotation schedules should be followed. Split hooved animals also aerate soil which helps with natural seed planting and growth. There is an entire focus on the use of ranching and forestry together with lots of science behind it, it used to be called silvopasture, but is now referred to as agroforestry.

Of course they can be destructive when not managed properly. The main cause of this correlation in most peoples minds imho is the fact that in the Amazon, such as Brazil, cattle ranchers were causing deforestation simply to create pastures. That is obviously wrong, but its not what happens in the US.

Do you have any references for this? I've honestly never heard of cows or cow-like grazing animals living in forests. I've only ever heard of them in grasslands.

To your second point, native biodiversity is definitely destroyed to graze cattle, that happens in the US and everywhere in the world.

They can be with proper handling and rotation. They are also vital for grasslands, not just forests. However, industrial raised beef is not good for forests, it's very very bad.