Why not overload operator+=() for std::vector?

I've started learning C++, so I don't know in my lack of knowledge/experience why something so seemingly simple to a rookie as what I'm about to describe isn't already in the STL. To add a vector to another vector you have to type this:

v1.insert(v1.end(), v2.begin(), v2.end());

I'm wondering whether in the real world people just overload the += operator to make this less verbose, for example to the effect of

template <typename T>
void operator+=(std::vector<T> &v1, const std::vector<T> &v2) {
    v1.insert(v1.end(), v2.begin(), v2.end());
}

so then you can

v1 += v2;

I also have this set up for push_back to "+=" a single element to the end. Is there some reason these things should not be done or are specifically avoided by people who are proficient in C++?