I have a folder on my PC that has each of my albums beneath it. Each album contains the photos I want on my iPhone.
I connect the cable between my PC and iPhone, start up iTunes, make sure the correct upper folder is selected (I use a different folder on my PC for my wife's iPhone) and sync them.
I wonder whether it's the transferring app or the displaying app or both that determines the display sequence of the photos.
I can only speak about the Photos app provided by Apple. That particular app uses the time/date stamp on disk for viewing photos when looking at the camera roll (or any folder/album viewed from the ALBUM tab). The Photos (Moments) when connected to an iCloud account uses the on disk time/date stamp from the camera roll and then uses the internal time/date stamp of the photos from the iCloud account (that haven't been saved to the camera roll). Last the Shared photos tab uses the internal time/date stamp to display the order of the photos.
I also wonder why so many people have "bad" answers to the question
I'm not quite sure you what are trying to say or imply. But as far as I can tell, there have been no "bad" answers. Only answers based on a persons experience with one or more apps over time.
and why it isn't just a Settings (app) option within an app. How hard could this be?
I've spent the last 33 years as a professional programmer. And that question is the one that makes every programmer simply shake their head. There are several possible answers to that question.
1) Has anyone before you asked for it? No? Then how would they know to program it?
(By the way, you are the first person I have come across that has asked for that feature. And I have been around iOS for quite a while now. To include spending several years as a developer for iOS).
2) Have enough people asked for it to justify the cost of the feature? No? Then why dedicate man hours and money to that issue?
3) Enough people have asked and the budget has been approved. When do we cycle in the new feature? During a major revision or a point release? Do we have to wait until other features of the app are stabilized before injecting the new feature?
I could come up with a bunch more questions like that, mainly because I have had to deal with this question more times than I can count, but I am hoping you see my point. There is never an easy answer when you are dealing with software that costs 100s of millions to make each year and you only have so many people to work on each part of it. Heck my primary project for the last 24 years has over $14 million dollars invested in it and we still don't have every feature that I want. As the chief architect and lead programmer, that means I have had to make some really tough choices to what gets put in and what doesn't because of budget constraints.
Is somebody trying to tell me that all photos displayed on my iPhone should be taken by an iPhone?
No. In fact my solution was done using pictures taking by several non-iOS devices. I wanted to combine those sources into a specific order for displaying on an Apple TV from my iPad.