It's not clear from your posts if this is clear to you or not, please forgive if I'm explaining something you already know: this flagstone issue has nothing to do with how chlorine is introduced into your pool. It's not the SWG itself that affects the coping, and reverting back to "chlorinated injection" would not solve any coping issue in and of itself. SWGs work by converting salt into chlorine, so you have to add that salt to the pool in order to make use of an SWG. It's the salt water that affects the coping. So if you tried SWG and then decided to abandon it for coping reasons, you'd also have to drain your pool and refill it, to get rid of the salt.
Ironically, a non-SWG pool, which never had salt added to it, will eventually end up as a salt water pool anyway. Salt is often found in fill water, and chlorine and acid (and perhaps other pool chemicals as well) all contribute salt to your pool, in various amounts. Salt doesn't evaporate, so it all just stays in your pool, and builds up over time. When I wanted to convert to a SWG pool, they measured the water and it already had nearly enough salt in it, and my pool was five years old at the time. I presume that was just from the salt build up I'm describing.
So regardless if you use a SWG or not, you'll have salt in your pool, eventually, one way or another (you already do). Your coping will either survive that or not. The only way to be sure to avoid this problem is to use a "salt-proof" material for your coping.
Further, an SWG pool IS a chlorine pool. Same-same. An SWG "makes" chlorine. Your pool water will still have just as much chlorine in it as before. The primary difference, is that an SWG makes and adds chlorine at a constant amount, just enough to keep your chlorine level where it's supposed to be. Pool guys and most pool owners spike the level of chlorine once or twice a week, so some days there's a lot of chlorine (too much) and other days not (too little chlorine).
And what your wife likes about the neighbors pool is the salt. That has nothing to do with the SWG itself, or how chlorine is added. She likes their pool because, in essence, she is swimming in soft water and it makes her skin feel nice when she gets out.
Some people add salt to a pool that has no SWG, just because they like the feel of the soft water. Of course, that would subject the coping to the salt.
Hope that all makes sense...