All you can do is keep them at bay, set boundaries and count the many blessings.
You pointed out some advantages to the brambles such as a screen for wind and noise. Here are a few more blessings of brambles.
1) The blossoms provide nectar for bees and other pollinators. Bees need all the help we can give them with the challenges they face. I have also seen wasps and bees actually eating the berries themselves in the summer months. I am not sure why. I think they like the sweet juice.
2) The berries provide food for birds and other wildlife- always a good thing.
3) You can enjoy them as well. Harvest the fruit. Be sure to wear heavy gloves to avoid scratches. Eat fresh or freeze for the winter. It's very simple to freeze berries. Lay them on a cookie sheet and freeze flat. Then transfer frozen berries to a zip-lock bag and label. I've also simple filled the bags and frozen that way, but they won't freeze loose, as they will be if you first freeze on a cookie sheet.
You could also make jam, jelly or syrup. These could make fantastic gifts for family and friends. Or maybe even sell them at a farmer's market. I believe wild foods are packed with more nutrition that those we cultivate.
4) The bushes and foliage provide shelter and protection for wildlife. Over the years, I have seen birds build nests in them and fledglings hide from predators under the thick brush.
5) The root system prevents soil erosion on that steep incline into the gulch.
I am sure there are many other advantages to the brambles behind your garden, but those are the ones that come to my mind.