The issue with having a strongman form of government lies in the succession after the current ruler steps down or dies. While the current leader may have done an excellent job steering the country, unless a system is created to outlive him, the temporary stability achieved could be at risk when his successor takes over.
Putin believes that journalists are the enemy of the state as they criticize the government's policies, and he is deeply suspicious of corruption. Furthermore, he thinks that clickbait journalism is broken and considers journalists a nuisance.
The removal of journalists for lying can be a slippery slope towards a lack of truth, and the elimination of both untruthful and truthful reporting means relying solely on approved government journalists. The American press has a history of bias, and the danger of removing voices from journalism is a loss of truth altogether.