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.