I wish this was the case, but the BBC news output has really dropped off a cliff the past few years. Going by the notifications I was getting a few months ago before I finally killed them off, they are pretty much reporting only on asinine shit about royals, people killing themselves and the occasional weird article that tries to put a shine on what our shitshow of a government is up to.
The BBC intended to educate and inform is unfortunately dead.
Cameron changed the rules of the BBC charter in 2015, and installed a load of Tory affiliated people. They first elevated Laura Kuenssberg to political editor, they then swapped the long time DG Tony hall for Tim Davie, someone affiliated with the Tories for decades. Then of course we had the Robert Sharp stuff with Boris. And we don't need to go into the drop in editorial quality.
Pretty much if something does not fall under the category of “might need my full attention within 5 minutes”, notifications are going to be off. So basically I have notifications on for all of my messaging channels (with most chats on mute), bank, security apps.
If theres any news worthy of a notification I expect the warning sirens to be on full blast and emergency broadcasts on every channel.