There is a long history of words being policed. Did the Church prevent the progress of information? Galileo in the 1600s, Darwin in the 1800s? The church still fights against the teaching of science in classrooms (evolution) and has led the effort to ban books all through the last century. Authoritarian governments currently try to suppress information - China is getting major attention and blacks out significant amounts. ( and the history of the cultural revolution is particularly dark )
But with the seismic shock the internet brought, editing out anything is virtually impossible (in countries without authoritarian governments that can control ISPs).
Of the major forces that suppress freedom, information, and ideas, there are multiple forces: social (including religion), government, and economic (which includes corporate censorship as well as firing speech offenders). All three are worth worry - especially in turbulent times.
I am not worried about government policing (in 'free' countries) as we live in an era of the least censorship and most mass communication in all of history. I am most worried about economic/corporate. I think the 'tolerance' side from social forces is the least worrisome, as it is the most open to debate, but obviously others find this the most worrisome. Social policing is the most visible, corporate/economic is the least visible.
That article is intentionally working for clicks & outrage to a certain extent to grab eyeballs. But I do think some self-awareness of language is important and good - for instance, I play in a co-ed rec sports league and I (and others) make an effort to use 'person' defense instead of 'man' defense. It is a small thing, but it is a good change that makes it more welcoming of all players (and the league is limited by the amount of women that sign up, so it is in everyone's best interest to make it more welcoming). Nobody is being forced to change or "canceled" if they do not. No history is being erased. But obviously the real world is very different than the culture of offense & outrage on the internet.
I'm genuinely asking, does the policing of words in reality make things better or worse?
Words have and always will be policed - I don't think this question recognizes the scope of the concept. It's not something that has ever not been a major component of human civilization.
