Sure there's selective sync, but that's an all-or nothing approach.
I like the way Google approaches this with their Google Photos service. X most recent photos are stored locally, and everything else is pulled down on the fly as you search/browse for them.
Which app are you talking about? The desktop app is merely an uploader. It doesn't really sync photos.
it randomly indexed all my wallpapers and threw them all into my timeline... i'm still not finished with the resulting cleanup.
though it might have been Google Picasa desktop app, i used both back then
That's not what we're seeing. Her phone gets to be 100% full, and deleting a photo frees up space. When we delete a photo, we get dire warnings that "this will delete the photo on all of your devices, and in the cloud too." I download them to my computer before doing this, so nothing is really lost. But it's annoying.
This is why I was amused by the breathless articles last week about how to "free space on your iPhone" -- essentially by clearing the cache by golly!
(If the 16GB is filled up 100% and things fail, that's an actual bug though. You might really have filled it up with stuff that doesn't use iCloud, leaving too little for the iCloud apps to work with)
BTW all of the above is orthogonal to "optimize for space / use lower resolution on portable devices" that others have helpfully mentioned.
Settings > Photos & Camera > Optimize iPhone Storage √