Per-file OOM badness

Not all games are necessarily amenable to perfect autosaving, although I agree that it should be implemented where feasible. But I can think of quite a few games where it would either detract from the gameplay, or at the very least would provide minimal or no improvement over the status quo:

* Undertale (the save mechanic exists in-universe, and removing it would completely wreck the backstory).
* Outer Wilds (no traditional progression mechanics such as leveling up or collecting items; you progress by learning more about the world and its history, so there's nothing to save other than a log of your discoveries).
* Most visual novels (usually, they automatically track which bits you've seen and let you skip past those; saving is at best a convenience function in most cases).
* Most turn-based RPGs (saving in-battle would be a Bad Idea because battles typically have a lot of highly complicated state that the player needs to be reminded of when they resume the game - better to just restart the battle from scratch since it's probably only a few minutes long anyway).
* Most racing games (individual races are typically a few minutes long, it's just not worth it).
* Any game that you can lose, and that doesn't have permadeath (if an autosave happens right before the player loses, the game may become soft-locked, so *some* amount of manual save-loading is required to exist, or else the game has to be very conservative about when and where it autosaves, and either way, the human playing the game has to think about what has or has not been saved at any given time).

Finally, I feel obligated to point out that kids know perfectly well when they can and cannot save. Depending on their age/maturity, they are either deliberately choosing to enter a section of the game where saving is not supported, or they are failing to plan ahead. I don't presume to tell parents how to raise their children, but in either case, you could choose to use this as an object lesson, if you felt it appropriate. For older or more responsible/mature children, it might also help to give them a 10-minute warning, if feasible. But, obviously, it's up to you to decide what works for your kids and your situation.

(I suppose some people might argue that none of the above games ought to exist. I shudder to think of what a boring world that would be!)