I hope it's not an issue that I'm replying to a month-old thread. I reviewed the previous discussion to try to avoid duplicating any of it.
When using pip with PyPI, calling pip a second time is much quicker than the first time, because it verifies that the requirements, including version constraints, are satisfied in the target environment and doesn't needlessly reinstall stuff.
Dependency links allowed the same behaviour to be implemented for private packages with dependencies on other private repositories: given a requirement B >= 3 and a dependency link that B was available from, pip could check if the environment already includes a package B with a new enough version, and only use the dependency link as a fallback if the requirement isn't already satisfied.
URL specifiers aren't useful for providing a fallback location to get a package from, because using one prevents the package from specifying a version constraint in the same way that was possible with dependency links, or with normal requirements available from PyPI. Curiously, discussion of version constraints in this thread has focused on how nonsensical it would be to compare them to the specifying URL, ignoring the possibility of comparing the constraint with the target environment.
The loss of this functionality means that anyone who was previously using pip to automatically install private packages with private dependencies now has to either forgo automatic dependency management (a large part of why one would use a package manager to begin with) in favour of recursively specified requirements files, publish their private packages somewhere so that pip can find them, or stick with pip 18.1 for now.