In short: RPG.SE's comment curation is a citizen-facing action to avoid the divisive habits in which many RPG sites frequently indulge.
RPG.SE is in a sweet spot where we can enforce Stack guidelines on comments.
RPG.SE's attitude toward comments is well within the Stack Exchange practices for comment curation. Some Stack sites are even stricter than we are (check out the history of comment curation on Christianity.SE or Gardening.SE some time) while others choose to be more lax, but often Stacks are unable to enforce comment curation to the extent they'd like because the volume of curation needed overall is too much for their mods and high-rep citizens to handle. In those situations, comments run amok are usually deemed a very low priority. RPG.SE is small enough the volume of comments isn't a barrier to curation, but has enough active high-rep citizens that its moderators aren't totally swamped with other tasks either. So let's look at the choice:
Curation is not strictly a choice made by the moderation team.
While only elected moderators can delete comments not their own, they aren't spending their days hunting for comments to delete: they don't have the time, energy, or inclination. That's what flags are for: tools for every citizen to bring things to a moderator's attention because we don't expect the mods to find all the fires on their own. Most comments get deleted because at least one non-moderator user flagged them. In this way, citizens tell the moderators how strictly they want the guidelines to be enforced on a day-to-day basis. (See below for links to the related meta discussions.)
Our choice to do so is a response to other RPG sites, not other Stack sites.
RPG.SE is remarkable in comparison to much of the online RPG community because it actively avoids arguments and tangents (focusing instead on the Stack's "well-sorted, actionable solutions to real problems" mission). Many people coming from other sites dedicated to RPG topics are pleasantly surprised at the contrast and they value our focused atmosphere. While it's true an occasional "+1 I liked this" wouldn't get in the way of that atmosphere on its own, experience has shown they give people the impression comments which don't help improve questions or answers are okay, and act as seeds for more troublesome comments.
So we curate comments aggressively for the same reason some other Stacks do: when a topic attracts an unusual number of out-of-line comments, pruning tangential comments of every sort is one of the best ways to keep the worse ones at bay. As a side benefit it keeps our actual questions and answers clearly visible without hiding important information in discussion threads or forcing extra unnecessary scrolling.
Aside: You'll find that our moderators respect comment upvotes. Comments with upvotes have to be especially egregious in order for a mod to burn them, even after flagging. This is how the community can indicate comments they value and want to see remain.
You can read more about RPG.SE's history of comment curation by searching through the meta questions tagged "comments discussion" and reading the FAQ on the subject. The list of "Related" links on the right side of this page will take you directly to some of those discussions.