"broadened the debate" is correct and usable in written English.
You can use it when you want to express that a particular event, person, statement, or action has caused the discussion of an issue to become more varied and comprehensive. For example, "The addition of a new perspective on the issue of gun control broadened the debate."
In 2013, Mayberry broadened the debate when she wrote a blog for a national newspaper drawing attention to the sexism endured by her and scores of other female musicians.
For example, in permitting more Americans to go to Cuba, the Clinton administration believes that it has broadened the debate within the United States and undermined somewhat the power of the Cuban American minority in Florida.
Though some people suggest that Iowa's stability has broadened the debate beyond the economy in the early stages of the campaign, the presidential candidates -- perhaps speaking to a national audience -- continue to focus on the financial struggles of Americans as they deliver speeches around the state.
Through two hours of testimony before an official inquiry into press practices, Mr. Grant raised new accusations that broadened the debate to include all of the mass-circulation British tabloids, not just those owned by the News Corporation, Rupert Murdoch's media empire.
Inclusion of practitioners and researchers broadened the debate beyond the medical practice to include research and the advantages and disadvantages IM had for science.
We may want to broaden the debate.
Perhaps most urgently, it would broaden the debate from the narrow confines of the settlements question.
She actually prefered Andy Burnham, but lent Corbyn her vote to broaden the debate.
The trust was determined to broaden the debate and prevent a focus on perceived failings of the corporation.
Mr. Kerry and Mr. Edwards are trying to broaden the debate beyond the absolute number of jobs.
It makes economic (and journalistic!) sense for the media to broaden the debate to include their views.
