Basically the NUL-terminator amounts to a 1-byte of wasted space -- which is almost always completely in the noise -- if you're using std::string for tiny strings you're paying at least 24 bytes anyway. There are just very few cases where that one extra byte matters.
I think the overwhelming opinion is that this 1-byte trade-off is better than the overhead of allocation and copying when you want to pass that string around. NUL-terminated strings aren't important in C++ because of C (well, not directly), but because they are essentially the ABI of countless existing libraries and the major operating systems.
> code that depends on NUL termination is not a thing to be proud of.
Whatever. Code that depends on NUL termination is ubiquitous.