I never understood why such people couldn't just, you know, not save.
In entertainment, restraining yourself from using particular features is something that is fairly unique to video games. Playing football, you wouldn't purposefully mess up a penalty if you were allowed one. Playing canasta, you wouldn't discard your jokers based on the card being too good. Most games tend to have hard rules designed around providing the best possible experience, no matter how many tools you use - in fact, many games tend to be designed first and foremost around optimal use of the available tools.
Some video games offer more leeway out of the box. Unlimited saving can be particulary pervasive because intuitively it feels like you're making progress, going from the start of the game to the end point. So it's tempting to use saves, which is fine; and it can become tempting to abuse saves, which can become tricky, because sometimes it happens to the point where you don't master necessary skills and fumble your way thanks to endless attempts or cheap tactics that ultimately aren't very fun or rewarding to use, a problem that only gets worse as the game difficulty increases over time (which tends to be the norm).
Even for someone who understands all that and would be inclined, intellectually, to exercise some caution, saving just enough to prevent frustrating moments but not so much to ruin the experience, lack of willpower is a potential issue. Most of us tend to make bad choices on a daily basis based on instant gratification - we drink too much, we smoke too much, we eat junk food, we stay up late at night despite knowing we have an early business meeting tomorrow. Video games are no exception.
While there is always the option to make a game harder for yourself with some self-control, disabling manual saving can sometimes allow for a more social experience. Would games like I Wanna Be The Guy or Dark Souls be as popular and reputed as relentlessly hard if you could quicksave your way through? Having an identical ruleset for everyone, a set of rules that enforce a certain level of difficulty, leads to more competitiveness.
This isn't to say unlimited saving is bad. I think both design choices are equally as valid and fitting for different games and different players, with neither being an objectively superior approach for everything and everyone.