I had vinyl with pucks and now in-ground plaster with SWC.
Some people like the physical feeling of saltwater (some say silky) and the extra buoyancy. Sounds like you've already read that you don't need a SWG to get this. You can just add salt to your pool for the nice feeling and higher buoyancy. For me, that would be a $100 reversible decision vs. $1200 with the SWG.
My SWG spec is 4,000 ppm with 3,000 minimum, and the pool builder said you won't even be able to taste the salt. That might be true at 3,000 ppm for different chlorinators, and I think this does vary by person, but I can definitely taste it, albeit not objectionable in any way. The upside is that many people find the higher salt easier on the eyes.
We have an SWG and like it, and for what it's worth here's my decision-making experience including a bit of advice I got from a poolie I play golf with, along with advice from most everyone I know. We have incredibly high residential pool ownership here, so most adult Australians know what an SWG is and have an opinion on it!
We don't have any water features with natural stone, so that's no issue for us. Another family member has a natural stone water feature that they leave turned off because of 1) noise, 2) evaporation and 3) salt deposits on the stone that have to be hosed and rubbed off. Salt corrosion of stone paving doesn't come up here, and if you ask, people look at you like you're from outer space. That said, people have stopped using the local sandstone as much, and prefer harder imported stuff. Lots of salt pools have limestone and travertine. I agree this is very regional - e.g. we don't have to think about freeze-thaw - but could you rinse everything down before winter, salt or not? Anti-salt people talk about the stone wearing out prematurely, but they're talking fewer decades. I think we'll be sick of our beautiful limestone paving and putting down iPhone paving or some such by then, haha. At any rate, a liquid chlorine pool also has salt in it, so this entire issue seems like a red herring to me, along with general corrosion of metal near the pool.
With respect to convenience, without the SWG I'd be lugging ~660 lbs (300 kg) per year of 12.5% pool chlorine, one way or another. We still keep a jug of chlorine on hand and dump a bit in before any kids parties (KimKats advice) along with a cup or two after.
My wife loves saltwater, and it's the normal market-dominant way to do chlorination here in Aus, so we have an SWG (pool builder throws it in, and no credit if we left it out - I think PBs buy them pretty cheap.) Without it, I would have found or figured out an adjustable metered liquid chlorinator.
My friend's view is that SWG's are solid, though he's not a fan of all brands, so DYOR. He did say that any controller can get fried by things like lightning and bugs nesting inside, and the $400 replaceable part (the cell) can burn out prematurely from poor choice of brand, or failure to clean the cell when needed. All models we looked at have reverse-polarity cleaning, so the cleaning of the cell is less frequent than it once was. Mine has not a skerrick of calcium on it after five months.
On my own, I would have stuck with fresh water, but my reason is just plain weird! I love letting all the air out of my lungs and seeing how long I can sit on the bottom! Can't do that in saltwater, cause I just float up no matter how much I empty my lungs in any saltwater pool I've been in. Maybe if I get skinnier?
Upward pH creep is previously mentioned and I'm currently adding a bit under a quart (litre) per week or 110 lbs (50 kg) per year, but as I learn from the experts here, my trend is down. If I had listened to the pool store, it would be at least double that because of their much higher recommended total alkalinity. I'm far from qualified to comment on this topic. I'm just a new-to-salt person who is starting to get it. I'm hoping I can get my acid down to a couple of cups (500 ml) a week. I've learned here that this will vary by pool, but if you're using acid now, expect it to go up a bit.
The saltier water can damage lawn and garden, so I put in perimeter drains as an extra line of defense in addition to the overflow line (we get some heavy rain here at times). That's probably overkill, but I feel good about it

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Most comments here say cost is a toss-up, which I think helps the decision be based on other more interesting factors. My numbers show it as cheaper by a fair bit, after considering initial purchase, cell replacement, electricity and increased acid use. That said, I think cost favours SWG only if the initial purchase and cell replacement cost is divided through 5 years (e.g. you're not planning to move house).
Summary for me is that if I build, buy, borrow, win, or take over any other pool... it will be SWG!