Tried my wife's Max and although the larger screen looks nice, it doesn't really offer any more usable space. You have the same number of icons on the screen, opening a website might show one additional word on a sentence. I guess it is kinda useful if you watch movies.
Why are the Max sizes so popular? Going from a 13" to a 17" laptop makes all the difference (work with multiple windows on the same screen) but I don't really see the benefit of having a bigger screen on the iPhone since it displays the same amount of info, icons, etc., but just a little bit bigger?
You pointed it our correctly - it is nuanced.
Where it makes no difference?
As you said, icons and all are the same. It doesn't really make a difference for day to day operations and things can be accomplished with no harm on a smaller phone.
Where it differs and larger is better?
As you pointed out, there are very few niche use cases which make the large screen better for said use case. Here is my observations having them all:
1) Immersiveness - it is noticeably larger when viewing content: instagram pops more to your face and you can spot the watches, earrings from the pictures posted on a larger screen. Photo editing gets better with the better/larger view of what you edit in lightroom.
For example, movie on the NYC subway - I can watch it on SE1 and i will totally get the point of the movie and will be able to talk about it.
But if you ask me: "remember there was this scene, behind the main actor was parked a 67 Chevelle? The same one was used in the last chase, so I suspect their neighbor was quietly helping them out to escape" I would say nope, haven't seen it - this small details pop out more on a bigger screen, so you kinda get more from your viewing experience.
2) Useful - remote admin of computers is easier to view/tap on a larger screen.
3) Battery - it is 2-4 hrs better than the smaller one. For example helps to still help family with remote admin even if you are hanging out in the evening.
4) 50/50% - text size. If you make fonts larger, it kinda fits a line or two more than the standard. It is 50/50 because it is not so obviously better than the smaller phone, but just giving that 1 extra line i am adding it here as a weak advantage.