When we compare C++ with Java, we see that C++ was not designed with implicit Garbage Collection in mind, while Java was.
Having things like arbitrary pointers in C-Style is not only bad for GC-implementations, but it would also destroy backward compatibility for a large amount of C++-legacy-code.
In addition to that, C++ is a language that is intended to run as standalone executable instead of having a complex run-time environment.
All in all: Yes it might be possible to add Garbage Collection to C++, but for the sake of continuity it is better not to do so.