Photos won't import an edit from Desktop

I like to keep my edited, often smaller, photos rather than the originals.

Don't use Photos. It's designed to do exactly the opposite. There are any number of pixel editors out there that will work as you want.

Photos is a Photo Manger with built-in non-destructive processing. It is designed to treat the original image like a film shooter treats the negative: Preserve it at all costs. You don't want to do that, you want to destructively edit (reduce file size) and not preserve the original. Ergo, it's not the app for you.

The workflow you describe above:

I edited a photo in Photos, renamed it and exported it to the Desktop but when I try to import it into Photos again

apart from being tedious would actually end up using more space - with double the number of originals - and is unnecessary, as you can rename image sin Photos.

"Preserving at all costs" is a good choice for some "creative" work but not all.

Is a perfectly reasonable attitude. However, Photos is designed for people who feel differently from you, and that is their perfectly reasonable attitude. Further, given that most photography is Jpeg, it's a defence against generational degradation.

Describing what I am doing as "destructive" is making a value judgement as though I am doing something bad

No need to be defensive. This is a descriptive technical term not a moral judgement. It means that when you edit some of the data is destroyed - hence destructive. Non-destructive processing means that the editor can always revert to the status quo ante. Again, not a moral judgement, but a technical term.

There is nothing wrong with how you choose to manage and edit your images. My only point is that you would have a better experience - and less work - working with apps that work the way you prefer, rather than ones designed to work the opposite way. Using the appropriate app means you'll have a better experience. Yes you can write a novel in MS Excel, but you'll have a better experience using Word, no?

Apple did not have a picture hosting service between 2000 and 2007.

What format?

Using iCloud is not a requirement, even with Photos. It's an option and one you can decline.

Homepage, as the name suggests was a website hosting service, iDisk was online storage. Neither was a 'picture hosting service'.