This sounds rather natural, I would say it fits in an academic paper or the news, but it doesn’t have to be in just those things. That’s just what I’m reminded of.
I would edit it a bit like this:
“All he does is mouth comforting, politically correct platitudes, nothing of substance.”
As for the bold parts:
“All he does is mouth comforting”
This is essentially “All he does is say comforting…” “Mouth” is just another way of saying,” say,” in this case. So, he says something that brings comfort.
“politically correct platitudes”
Political correctness is difficult to explain. Even the definition is long:
“the avoidance, often considered as taken to extremes, of forms of expression or action that are perceived to exclude, marginalize, or insult groups of people who are socially disadvantaged or discriminated against.”
Although that is the only definition, I have seen this term used in a negative way by some political groups all the time. If someone is being “politically correct,” they are seen as saying what other people want to hear. I could be wrong though, I’m not too big into politics.
Platitudes are basically things that have been said so often that they are no longer interesting or thoughtful. Overused words, usually having to do with morals. They oversimplify subjects that are complicated. There are numerous online examples of platitudes. One I saw was “break a leg.”
Basically, by him mouthing (saying) politically correct platitudes, he is saying what he is expected to say, both politically and morally. Things people will most likely agree on, since it’s politically correct.
“nothing of substance.”
Nothing of value, nothing of worth.
That’s my interpretation, I hope this helps, if not I’m sure other people will reply with something better. Good luck!