I'm a huge supporter of a true save-anywhere system.
If I need to quit the game, I don't want to lose progress.
If there's one hard part that's giving me trouble, I don't want to continuously repeat the easy part before it over and over again just to get back up to the part I'm having trouble with.
If the dialogue options are unclear, I don't want to be stuck with choosing the one I didn't mean to (this isn't really a problem if the dialogue choices will show the full text though, but I hate it when the choices are just icons or short phrases that don't really tell me what the character will say if I pick it).
And of course if the game is buggy I like having a ton of backup saves that I can fall back on to minimize the amount of gameplay I lose from trying to get around the bug.
Having said all of that, I have reloaded a lot if I was having trouble with a fight (trying different strategies until I found something that worked) but I never really reloaded a lot to win at random events like opening a chest. I don't mind at all if the game pre-generates random events and saves the results in the game save because I wasn't going to keep redoing the random event anyway. I can see how that might be addictive to people who like to gamble though, and if the game wants to discourage people from getting addicted to gambling in it then I think that's okay.
The main issue for me is that people should be able to save their progress whenever they want so that they won't lose a lot of gameplay if something happens.