Hands Off Hartlebury Common

I don't assume that anyone's 'truth' is the truth, which is why I'm interested to see how the work on the common pans out.
An open area of oak fringed common, heathland, that has traditionally been well worn by the public for generations will still change over time given certain factors.

On any of these areas you could graze or not with varying results due to types of grazer, soil and plant structure, weather exposure, human traffic, new species introduction and length of project time. Rarely would two sites be exactly the same so what works on one site will damage another and vice-versa.
With the main damage being down to weather conditions and human foot traffic, I did sometimes wonder if the grazing scheme was simply to discourage visitor numbers (but the common seems well used still) as well as being a way to advertise that something is being done by putting work on public view.

What would you do if an historically naturally sustaining area had an influx of invasive flora, and existing flora and identity of the area was threatened by such? Should it be left to itself and ignored or not?