TLDR Edit; Initial response seems that the most important thing is to be honest and clear, and trust both readers and authors to interpret what they need from it. Trying to moderate response is liable to do more harm than good, and being nice is (slightly) less important than making sure people have any amount of reliable feedback, keyword reliable. Thanks all.

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I don't really know how much they influence potential readers, since I usually find new stories by following the Favorites lists of people who seem like-minded/reputable and checking out covers I don't recognize. 

My issue with reviews is that the feedback is visible, (possibly) critical to further visibility, and crystallized. I don't want my opinion potentially bouncing away new readers, sinking new ships, hanging around if it becomes invalid, and most important, I don't want anyone changing their style to try and make some anon happy. 

Every 'bad' story is somebody's nostalgia baby. We all have people and things we wouldn't have enjoyed if we'd seen the reviews first. I don't want to be the reason someone doesn't enjoy something.

But I DO want to show appreciation and elevate the stories I find and feel are deserving.

Is this feeling justified? Is it worth leaving an unhelpful/generic review just for the sake of traction/rating and providing deeper feedback in a DM, or is leaving it all hanging out really not that big a deal? How much would a good/bad/generic review have actually influenced your start here? How much does sandwiching praise/criticism actually affect reception, is concise language or flowerier prose a better cushion?

Personally I would love honest feed back. I'm new to this and am working hard to improve, so typing out a critique, in the chapter or private DM I would like to hear it.

The rating system without critique is different. A 0-3 star rating with no explanation seems like a kick to the ego for no reason.

I'm not everyone though, this is just my take.

I second RJDorey's take. As an author, I actually appreciate the honest (even if its sometimes harsh) reviews and comments I get. Those are the ones that make me really think about how to make my writing better. 

As a reader, if I was going to read the story, I am going to read it anyways. I do find that the constructive and fair reviews are the ones I automatically upvote, as opposed to the ones that coddle the author. 

Your opinions matters. A 'bad review' isn't going to sink a fiction past a certain point (besides, that is what review swaps are for) 

So just write your feedback to your heart's content. 

But eh, that's also my two cents. I might not be in the majority!

What you enjoyed in the story.  Anything touching that is golden.  Characters?  Relationships?  Technology?  Setting?  Action?  Writing style?  What drew you in, made you say "this is the one I want.  This is what brings me the kind of enjoyment I want in my entertainment."

Royal Road gives you a guide that's something like you'd get in a classroom.  Sure, helping authors refine their craft is great.  It's useful, it hones our skills, and that in turn helps us entertain better.  

But where it's really at is the entertainment.  We're not writing technical manuals.  Well, some of us might be (fictional ones), and yes there IS an audience for that.  Point being, we write to bring enjoyment to the reader.  Be it with suspense, action, horror, comedy, drama, wide spanning intrigue, or simple cozy stories.  We want to hear what you liked in your own words.  What let you fall into the story.  

If anything breaks that reader trance, like a metaphorical kick in the gut- something like inserting (current year fad/politic thing/religion thing) into a blatantly fantasy/cyberpunk/whathaveyou story without making it seamless- that needs to be brought to our attention, too.  

If I made Doc Z start talking like a Valley Girl, like, all the time, and start becoming a social butterfly I guarantee there would be outcry and demands of WTF, OVER?  That does not fit the character of the story, so it will not be happening.  When the story goes off the rails and the reader knows it, it's obvious.  And it's a very bad thing.

TL, DR; what'd you like most about the story?  And what booted you out of it like a bad date?  Those two things, we want.

Depending on the goals of the person writing the review, a review can have two very different purposes. I believe the primary purpose of a review is to inform other potential readers of the expected experience with the story. If the reviewer enjoyed it. If they didn't, then why. Negative reviews are often the most informative here. I've often bought things online based on negative reviews, because the thing the reviewer was complaining about was a selling point to me. If the review says the pacing is slow and spends too much time in slice of life, well, that's not a negative. People who like slice of life and slow burn would like that. If the review complains about grammar, then someone who is easily irked by bad grammar would know to skip it. 

The other purpose of a review, and to me this is secondary, is to tell the author places they could improve. I find this secondary for a few reasons. First, the vision of the author and the desires of the reader may not align. A reader that prefers sparse text and minimal descriptions is not going to like a writer that waxes as descriptive as Tolkien. The author should not change for that reader, and the advice to tone down descriptions should not be heeded. However, if that's a repeated complaint, the author may want to keep an eye on such things to be sure they are not waxing overly purple. On the other hand, complaints that sentences don't parse well, or that there are logic flaws in certain events are beneficial to the author so they can improve clarity.

Unless the review is talking about mechanics, in general don't change the story for one or even several reviews. Stick with your vision and stay the course. There are some circumstances that will always anger readers. Animal cruelty, slavery, sexual violence, and other specific events can trigger bad ratings and reviews. That doesn't mean the story is bad or wrong for containing those elements, just that readers react strongly to them and that will be reflected in the ratings/reviews.

Just me but I very much value honesty and clarity. 
Too often people either try to use kid gloves or on the end of things get to be cruel and derisive. 
Neither of those is particularly helpful to the author. 

Just be honest and clear, if something doesn't make sense or doesn't feel right, just saying so is what helps. 
I have a friend going over my first book and he has been extremely helpful because he is above all, honest. If something doesn't make sense to him he says so. 
He also understands that it is up to me if I decide to implement his feedback or not and that is what makes it work. 
As a reviewer and a writer neither of you can take it personally, otherwise you will gain nothing from it.

Here's what I found worked for me when I did swaps (these days, the inclination is rare):

I try to comment on every chapter I read with observations/encouragements/critiques/suggestions. By the time I reach the agreed-upon word count, they probably already know how I'm feeling toward their book. At that point, I determine what rating I would honestly give them. If I'm feeling generous, I'll give it a courtesy bump, because we're all amateurs here. But if I can't generously give the story at least a 4.5, I message the author privately. Usually, we just agree to go our separate ways. Not a good fit. No hard feelings, plus, they get some honest feedback. 

Some people might consider this rating manipulation, but I think it's more akin to, "If you don't have nice things to say, it's often better to say nothing." And if you're gonna say hard words, it's kinder to say them in private.