If what you're after is that close to 'hard' ironman, what exactly is the point of even having it, then?
As to 'inconvenient and unnatural', speak for yourself. Saving a game/ongoing work/other info is as natural to me as e.g. searching the web.
And the point here was that if the saves are fully automatic, they are almost exactly as bad as a single ironman save wrt bughunting. Your once-a-week save days later is not particularly more useful for debugging than a single ironman save. If you even remember to take and store that save afterwards.
One-button saves exist, press F5.
Basically, you can already have most of what you're proposing by playing with a larger number of auto-saves and foregoing manual saving entirely. This seems to be what you're after, isn't it?
Given the choice of replaying a busy week in-game, or living with some moderate catastrophe (like losing a new base, or somesuch), it's not clear the catastrophe loses. Mods like Piratez have a ton of management going on, not to mention big swings in what the RNG gods give you.
From what I've seen, people tend to pick a path/captain/codex and follow it even after reloading, and the big choices aren't nearly as frequent as to be weekly, so it's not really that these bronzeman autosaves would offer much in terms of additional replayability. IMO, a save at the exact point of decision is much more convenient and tempting than having to play half a week to get to that point.
The OP should've made the point(s) clear.
Standard save mode is: manually save any time, no limit, reload anytime.
Ironman mode is: only auto-save every 10th day, 1 save, no reload.
Suggestion is something like: only auto-save every under 4 days, 10 saves, reload anytime.
That looks between both, which is distinct enough.
It's the norm--what most players do, that matters. Again, I don't think that they keep hundreds to thousands of saves. For me to believe that that's the norm, saving would have to take only about a couple button presses and no real need for typing due to the game automatically writing "new save ##".
I mean, it's obvious, so I'll assume that the Devs found it unfeasible to do--which is why I considered auto-save every 4th day reasonable--but for them to incentivize players to keep a massive amount of saves, they could implement an unlimited one-keypress save function. If the once-a-week saving isn't effective, the idea goes back to save once a day.
Where's the Geoscape multiple-slots frequent auto-saving? The disabled manual saving option? The Geoscape auto-saving with frequency higher than 5?
Ideally, we'd be able to configure the saving methods at the start of the game and opt to only be able to do so then. Ironman could be replaced for that, and most players would prefer something not extreme. That would be outstanding--shouldn't that be feasible for a 20+ YO game? (Are you some Dev? What's your perspective on that?)
That depends on countless factors, such as what the player may be feeling at the time.
"Paths" don't have to necessarily be important-feature related, but regular gameplay decisions.
Ironman modes are popular for not allowing that much freedom, which is why they are much more exciting.