This will have side-effects, most of them unwanted ones.
While comment threads get long and then tend to be cluttered with off-topic or inappropriate or whatever content, they also are a vital line of communication not otherwise present.
That might sound like an advertisement for a violation of guidelines? It is not meant to be that. Some use cases come to mind:
- Our "welcome to new users" is a borderline case where part of the comment is not "suggesting an improvement" but meta-ish talk explaining the site
- If a post, especially an answer, is just wrong or "not even wrong" then stating or explaining that is not an improvement suggestion
- adding an explanation for downvotes or votes to close are sometimes useful for improvement; if it's about off-topic posts, then what is the "improvement"? Deletion?
These are not the only usage scenarios imaginable that would not fit too perfectly into the "suggest improvements" version of "add a comment"?
The comment policy is formulated quite strictly and enforced with varying adherence to that strictness, but certainly not followed too loosely on this site and my impression is that the mods do use their mops quite effectively and efficiently; that is the system seems to work relatively well (also in comparison with other sites). If chit-chat appears, and I've seen it appear from high-rep users and even mods as well, then it nearly always disappears into oblivion quite quickly.
That said, I often find the comments quite valuable on their own, in conjunction with the answer or in their own right (I know that this is also a conceptual problem). But the change proposed is mainly designed to do one thing: reduce the number of comments. Well, "reduce the number of [low quality] comments" is the stated goal, but the result to be expected is the overall number of comments being reduced.
Finally, low quality comments emerge and have to be seen as a social problem: people not knowing or consciously violating the rules; rephrasing a button text to nudge people into better behaviour is an attempt to fix social problems with technology. People inclined to agree to that might want to read
Howard Rheingold: "Why can't we use technology to solve social problems?"
Max Oelschlaeger: "The Myth of the Technological Fix"
and weigh the arguments on that.