While I was way too young to remember, isn't it possible some in the Republican Party might not have considered broadcast of the Watergate hearings to be in the public interest?
As for your comment that Republicans would not have found network coverage of the proceedings to serve the public, that's nothing more than a case of reading into history our present-day political animosities. Sure, Nixon and the Administration didn't like it. Sure, the Republicans in Congress would have done everything they could to prevent it. But if the atmosphere that prevails now on Capitol Hill and in the White House had carried the day then, there would have been no Watergate hearings to start with. Besides, network news departments had a much stronger firewall than today against pressure from their employers and the Government to curtail news reporting unfavorable to a particular party (that has pretty much gone by the wayside now, swept away by the triumph of cable news and the Internet and the fiercely competitive media world). If the FCC had become aware of such attempts at censorship, it would have strongly warned the networks and broadcasters not to comply, for fear of violating things like the Fairness Doctrine, which was abolished in 1987. From another perspective, it would have amounted to political suicide for a Republican legislator to come out publicly against the networks carrying the hearings (While this may sound overly political, Vice-President Agnew and Press Secretary Ron Ziegler had already cried wolf far too many times against supposed ideological bias and slanted reporting on the networks' part; many Americans, even conservatives, had tuned them out by this time). Whatever we think about the matter today, the consensus among broadcasters, the public, and even advertisers was that broadcasting the proceedings took precedence over all political and economic considerations. We were, in other words, a far less cynical, more respectful society than is even possible nowadays.
What you have to remember is the Republican party of 1973 was nothing like the party of today. Senator Barry Goldwater, the gold standard of Conservative thinking at the time, wanted Nixon's head on a stick as did many Republicans at the time because they recognized the abuse of power. If was only from within the administration that fired accusations of bias; that is where we get the term "a non-denial denial". You're not denying what was done but you will question the messenger's canine heritage, or lack there of.
Speaking of Goldwater, John Dean seek the advice of Goldwater before going in front of Congress. Dean was torn between betraying his boss or facing contempt and disbarment. Goldwater's advice was simple, "The Son of a Bitch lied, hang him". There was also a story of a private meeting between Goldwater and Nixon at the oval office. Goldwater made it clear to Nixon that he would be impeached, days later Nixon resigned.
The morale of the story, if Nixon had Mitch McConnell, the Republican party as defined today, Fox News, Rush and the rest of the pundits he probably would have gotten away with it.