(Sorry for the wall of text, folks, but Dasale asked.
Also, I want to preface this by pointing out that I'm mentioning a multitude of different save restrictions below and am doing so haphazardly. However, my biggest grief is certainly with checkpoint-only saves. But any limitations at least irk me.)
It's an immersion factor to me, even if I appreciate how other people find manually saving something that breaks immersion.
I believe in saving often but loading as infrequently as I possibly can. This gives me the choice of what I want to replay. If I just completely borked something and die but was having fun, well I'm going to choose to replay that even if I have a newer save that lets me skip it. If I just got to the end of an unamusing sequence of the game and it crashes or lags causing me to fall in a pit, or, yes, even if I borked something, I want the option to skip it. I may not take it, because I like to challenge myself, but I want the option. This is because being forced to replay something I did not particularly enjoy is anathema to me. I have very little "playtime" and I want to make the most of it.
Being forced to replay a segment of a game is a punishment for the player, and nothing more. It certainly doesn't make sense any more than being able to reload at whatever point in time in the past that I want to makes any sense. But, in the case where I'm being punished by having to replay something without any choice in the matter, it strips my immersion in the game entirely. I just zone out for the repeats - detach from the game. And, even if I'm enjoying the game, I find replaying segments to be generally a negative experience that breaks the rhythm of the game. (Although I break that rule intentionally, as I'll mention in a bit.) That is, in part, why I only replay games years apart and I've forgotten enough of the experience. This is true of even the best games I've ever played.
Instead of a manual save breaking immersion as it does for some, for me it's my worrying when I'm going to get to the next checkpoint that breaks my immersion. (And the same goes for save rationing systems like in Hitman.) Instead of focusing on the game, I get distracted by trying to get to that next save.
Additionally, I find having saves wherever I want allows me to explore more. Checkpoint systems punish you for exploring and taking risks. I like to experiment - try things that perhaps the developer didn't intend, or simply explore a world for the sake of exploring. But those things have real risks and can end up with a grizzly death or with you stuck in the scenery or crashing your game. With my own manual save, I can now go back to just before I did something experimental and continue.
Furthermore, I like to experiment with dialogue. Dialogue systems are always, _always_ flawed, and it's exceedingly common that a dialogue choice isn't what you intended. I'm not referring to unintended consequences - those are good - those are C&C. I'm talking about when the response sounds like what you want to say, but the game writers decided it was actually completely sarcastic, or some other distortion of my expectations. Now I just had my character act in a way totally in disagreement with my role-playing. So, I want to reload from just before I started the conversation so I can rectify the game's mistake. Other times, I just want to see what would happen if I said this, even if it's not in character and not what I would allow in the true telling of events in my game. The save allows me to try what-if scenarios that I enjoy without penalty.
There was a good article (or at least mention in an article) on RPS recently regarding how checkpoint-only save systems damage exploration and experimentation, but I can't find it right now, unfortunately. Nevertheless, it echoed my thoughts well.
Lastly, I'm on-call for my job 24/7. At any moment I may have to stop. Leave the game running in the background? Sure, I do that a lot if the game allows me to alt-tab or run in a borderless window. But this doesn't fit all situations. Frequently I'll have to boot onto a different partition. Or I'll need to work straight through the night and not have time to get back into the game to get to the next checkpoint before I need sleep. Or I need all system resources available for the dev project. Again, I'm punished because I'll have to go back to whatever arbitrary point the devs chose.
I've been gaming since the early 80s and am decently competent. So my reloads are very often more about UI limitations, game (or mod) bugs, and my enjoyment of experimentation and exploration (game-world and dialogue). Checkpoints are fine so that people who do not want to be bothered with an out-of-game concept can ignore saving …as long as I ALSO have the choice to save anywhere (and the load continues from that point and not just from the last checkpoint). Some people find save-anywhere damaging because they abuse it. Well DON'T ABUSE IT. It's cheating. I personally have no problems with SP cheating. But don't complain the game is too easy or not engaging if you cheat. If you abuse the system, you better be prepared for the consequences. If you enjoy the game more because of it, well kudos.
I appreciate that you don't consider the save system to be a major factor when considering cross-platform games. But to me it's _at_least_ as important as anything else Mr. Francis explores in his article.