The media examples provided, Time and CNN are not held accountable for disinformation. They spread disinformation and propaganda regularly, especially CNN. Most "old" media companies do, MSNBC, ABC, CBS, FOX, The New York Times, etc. Trying to stop disinformation is always problematic. The main problem is, who gets to decide what is misinformation? I would rather see all of the opinions and facts available and then make up my own mind.
There would be less of a trust issue if the media and governments weren't wrong so often. climate change is real, the cause is not so clear cut. When the government scientists are caught either cooking the books or using data from sensors that are known to be defective, their credibility erodes. The governments told us that the SARS-CoV-2 virus that causes COVID-19 came from a wet market in Wuhan, China. There was early evidence that this was not correct and that the virus actually came from the Wuhan Virology Lab. The people that listened to that evidence were called conspiracy theorists. Eighteen months later, the evidence is more clear and the "experts" are starting to admit that it probably came from the lab. Fauci adamantly denied U.S. Government funding of change-of-function research at the Wuhan Virology Lab. Months later, evidence is produced to show the U.S. Government did fund the research and Fauci knew and lied about it. Fauci has been wrong on nearly every claim he has made about the virus. We had nowhere near the deaths he predicted. The U.S. would have had far less had New York Mayor Cuomo not murdered 15,000 in nursing homes. Governor Whitmer did the same in Michigan but I don't think we have the numbers yet because she hid them. The FBI planned to kidnap Governor Whitmer and then foiled their own plot and arrested incompetent followers of the FBI plans. A clear case of entrapment. The FBI had 12 paid informants, some made $50,000 or more. Some of those paid informants were put in leadership roles in the "militia." One FBI agent tried to have one of the informant's frame an innocent man and to delete the texts detailing the frame. Thankfully the guy didn't delete the texts. The lead FBI agent has been fired for domestic abuse, unrelated to the plot. The incident and firing do expose his character though. All of these things make it hard to trust anything the government or government scientists say. There is no science to support the lockdowns or vaccine mandates. You can still get sick, hospitalized, and even die after being fully vaccinated. The virus is 99.8% survivable. More for the young and healthy and less for the old and unhealthy. The lack of efficacy for the vaccines caused the CDC to have to redefine vaccine on their website so they could still call them vaccines. The Pfizer vaccine is the only one with FDA approval. Federal law states that if there is an FDA approved vaccine, the use of others under Emergency Use Authorization is forbidden. They are still using the others, in violation of Federal law. There are likely similar laws in other countries.