Even if I were to accept the official Watergate story (which I do not considering that the star reporter was Naval Intelligence just 2 years prior to his 'big break') "Deep Throat" was not running an alternative information outlet in public.

Accepting this makes it trivial for non-governmental elements, or foreign governments, to put up e.g. @AltStateDepartment for every single governmental org. That is not going to promote "stability" of our system. In fact, this is precisely what I would do if I wanted to entirely demoralize Jane/Joe public and undermine /the public and democractic state/.