American culture at one point decided that machines were the only way to control the wilderness. Happily, we seem to be unlearning both the machines and the control lessons.
I saw (fenced-in) goats trimming grass in the Berkeley Hills as far back as 2000. I'm sure people were doing it long before then.
> why isn't this done more often
Possibly because it's hard to make sure than none of the goats escape, breed, and wreak havoc on the native species. Eradicating invasive species can be unbelievably expensive and brutal (e.g. helicopters and machine guns), even on small islands. Hopefully they've embedded GPS trackers in all of their goats, but I still suspect that they're taking chances.
In areas where fires haven't historically been as bad, it hasn't been necessary. A decade-long drought and environmental changes make things done elsewhere (Bay Area, for example) appealing in a new region.