Just a note:
1) Internal software (either used internally or presented as a service) sometimes get released publicly, having vulns tracked via CVE would make the entire life cycle much easier to manage when things go public.
2) The world has already moved to a services model, most apps aren't that useful without some online service/API, so there is definitely value in knowing what services I use are vulnerable.
3) There is also a strong push for security transparency (e.g. the CloudSecurityAlliance has several hundred STARS CAIQ entries in the registry and I know that most cloud services has one as many large companies/governments now require such an entry prior to purchasing the service), so this is something the industry will be doing, ideally CVE should be a part of that.