Interesting question!
I don't actually like the way I phrased it. When I re-read the post I thought it was a bit awkward. It uses too many soft words -- both "feel" and "convince". I am trying to remember to not write that way, with so many heavily qualified and disclaimed opinions. The use of the word 'feel' is the wishy-washy hedge that I really don't like here, but yes, it is trying to disclaim and the certainty of the point, to sound less imperious. (It's also an awkward word because the phrase "the paper feels" is awkward English. Papers don't feel. It makes sense in context but still sticks out like a sore thumb.)
This habit has been infected the way I write everything over time and I don't think it's necessary. It's redundant: it's implied that everything someone writes is their 'take' on the matter. And it reflects trying to write exactly the words you would say if you were speaking, instead of using the slightly different language of written English, which doesn't need so many qualifications. I think the older I get the more I forget how written English works, like I'm losing touch with how to sentences that aren't just transcribed speech.
Although, there are some subtle differences in the connotations of a few ways of phrasing the point.
* " This paper feels very unconvincing" -> the paper has a quality of in its text, which anyone could recognize.
* " I find this paper unconvincing" -> the unconvincingness is a quality of my body of knowledge.
* "I'm not unconvinced by this paper" -> the unconvincingness is a quality of how I reacted to it.
* "This paper is wrong" -> I have really good information that the paper is wrong, it's not just a layperson's hunch. I don't have a physics PhD and I've never felt like a person who is fully allowed to say things like this, even though I am pretty sure it's true.
* "This paper feels wrong to me" -> same thing but with one of those disclaimer words to undermine the claim.