Hey Ontario, I'm a former BC'er.
Some people like the physical feeling of saltwater (some say silky) and the extra buoyancy. Don't get fooled that you need a SWG to get this. You can just add salt to your pool for the nice feeling and higher buoyancy. That's a $200 reversible decision vs. $1200 with the SWG.
My SWG needs 4,000 ppm 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.
We have an SWG and like it, and I'm happy to share my decision-making experience including a bit of advice I got from a poolie I play golf with, not to mention that with incredibly high residential pool ownership here, 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, 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 why wouldn't you rinse everything down before winter, salt or not? Anti-salt people talk about the stone wearing out prematurely, but they're talking 10 or 20 years. I think we'll be sick of our beautiful limestone paving and putting down iPhone paving or some such by then.
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 leave it out - I think PBs buy them pretty cheap.) Without it, I would have found or figured out an adjustable metered liquid chlorinator. My poolie mate talked me out of sensor style automation because fixing/replacing those is the sugar on his donut profit-wise. (that and the fancy chems he sells to the posers who haven't discovered TFPC.) I was just looking for simple (SWG fits that), low-cost (he agrees cost is a toss-up), and not putting chlorine in my car is a bonus. We have the pool light switches inside by a window that looks out onto the pool, so that feels automated to us! He also said that if you like tinkering with network/iPhone/ipad stuff, then buy it as a luxury.
Marian mentioned season-length, and it makes sense that the economics would change for that. If you use it less it lasts longer in terms of years, but probability would say that if you own it longer, failure becomes more likely (e.g. lightning, sub-standard component, bad luck!). The cell erodes based on usage, wearing out based on how much chlorine is produced. The easiest way to think about the cost aspect (IMHO) is to accept it's a toss-up, so you can make your decision on other more interesting factors

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My friend's view is that SWG automation is adequately 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 low flow over the cell (people running VS pumps too slow, plugged skimmers, etc.), 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 nearly two 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.
I also learned here (after my decision) that the SWG usually adds to upward pH creep, so you're likely to be adding more acid than you would if using liquid chlorine. 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.
I only offer this for what it's worth. I'm not experienced enough to recommend anything. Go read pool school and stuff. The team here has boiled it down so it's not a huge read, and it's real straight talk. You'll get good answers very quickly. If you don't believe it or want references, you can dig as deep as you want on this forum. You'll find balanced answers with honest representation of unknowns and healthy respect for debate and skepticism. And when they say "Stay out of the pool store," they're right!