I wonder how much string manipulation you'd have to be doing to see a benefit. I still can't use C#6 everywhere at work because some teams insist on being in VS2010 / 2012, so I'd be pretty worried about going to C#7.
Both approaches have benefits and drawbacks, but apparently copying the sub-string seems to be best for the vast majority of cases and you only benefit from the shared buffer in select cases (also it's a great memory leak opportunity if you don't know how it's implemented). So I guess it makes sense for .NET to add the capability (in a more general form that also works for other things) instead of only having one or the other.
Span<T> conveniently side steps this issue by only existing on the stack, meaning that you can't stash away the span somewhere and accidentally keep the underlying buffer alive longer than necessary.