"I think it is a field requiring a lot more study to determine if a fox presence is beneficial or detrimental to the ecosystem it inhabits"

It's not detrimental to the ecosystem it inhabits, but farmers knock an ecosystem out of equilibrium when they destroy fauna, flora and habitat. In that respect, they're trying to eradicate the indigenous forms to grow new ones.

All animals, including foxes are part of an intricate food web that is basically a flow of energy that starts when a plant captures photons from sunlight and goes up the food web to apex predators; the big beasties that eat the big herbivores. Apex predators create a trophic cascade which limits the abundance and alters the behaviours of prey... for instance deer in Yellowstone changed their browsing habits when wolves were reintroduced in order to look out for them and avoid ambushes. This meant saplings reached maturity, insects populated the growing trees nd the songbirds returned... you get the picture.

A fox is not a natural apex predator although we have forced it into that role as our apex predators are wolves and bears, but we killed the last of those off years ago. However, a fox is still vital to what remains of the ecosystem as they prey on animals that might otherwise get out of control such as small mammals and birds. They are vital to preserving what is left of our indigenous wildlife, as are all our wild animals. That some people think they are a pest is because they occasionally have the temerity to wander into our artificial landscape and opportunistically take prey. They're just doing what foxes do.

The problems the UK is having with deer could be mitigated if we introduced Lynx back to the landscape as Lynx are deer specialists and would control populations that are currently getting out of control and perhaps even make progress in eradicating introduced deer species that do damage to saplings and other native plants. You'd never see them either, they are shy and don't like humans (who can blame them?).