You found a wallpaper that looked perfect in the gallery, set it, and now the hair edges are furry and the gradients have visible steps in them. Nothing is wrong with your phone, and cropping it differently will not help.
Anime art is unusually good at exposing a bad file, because it is built from clean lines and flat colour, and those are the two things that survive scaling and compression worst. Here is how to work out what happened and what to do about it.
The three separate causes
They look similar on screen and need different fixes, so it is worth telling them apart.
Upscaling. The file is smaller than your display, so iOS stretches it to fill. Line art goes soft, hair edges gain a faint halo, and everything looks slightly out of focus even though nothing is blurred.
Compression. The file has been saved and re-saved. Large areas of smooth colour break into visible bands, and fine detail like lightning or fabric texture turns into mush. Sharpness is fine at the edges but the flat areas are wrong.
Cropping. The image is large enough but the wrong shape, so filling a tall screen means zooming into a small part of a wide picture. Effectively upscaling, but caused by aspect ratio rather than size.
Look at a hard edge for the first, a smooth gradient for the second, and the framing for the third.
Why anime art shows it worse than photographs
A photograph is full of noise and texture, and both hide compression damage. Anime art is the opposite: hard black outlines against flat colour fields, which is the most demanding possible content for a compressed image.
The flat areas show banding because there is nothing to disguise it. The outlines show softening because there is nothing to blame it on. A photo can lose the same amount of data and look fine.
This is also why an anime wallpaper that looks acceptable on a laptop can look poor on a phone. Phone screens are physically small with a high pixel density, which makes every flaw smaller but sharper rather than hiding it.
Where bad files come from
The usual routes, roughly in order of how much damage they do.
Screenshotting a video is the worst. Video compression is designed to discard exactly the detail anime art is made of, and a paused frame carries none of the original resolution.
Saving from a social feed is next. Most platforms recompress on upload and again on download, so what you get is a copy of a copy.
Image search results are unpredictable. The thumbnail is a resize of something, and the something may itself have been a resize.
Chat apps compress by default on send, which is also why forwarded wallpapers arrive worse than they left.
This is what breaks live wallpapers too
The same detour that costs you sharpness costs you the motion. A Live Photo is a still plus a paired video file, and sending it through a chat app, uploading and re-downloading it, or opening it in an editor that does not understand Live Photos separates the two. You get the still, the pairing is gone, and the wallpaper sets as a flat picture with no explanation. Save from the source app straight into Photos, then check for the Live badge in the corner before you set it.
What actually fixes it
Start from a large original. That is the whole answer, and everything else is a workaround.
If you cannot, three things help a little. Choose darker art, since banding is far less visible in shadow than in a pale sky. Choose busy art over minimal art, because texture hides damage that flat colour exposes. And avoid pieces whose main feature is a fine effect, like lightning or rain, since that is what disappears first.
What does not help: sharpening filters, which make halos worse; upscaling apps, which invent detail that was never there and usually look plasticky on line art; and re-cropping, which cannot add back information.
What a good file looks like on the phone
Worth knowing what you are aiming at, since most people have only ever seen the damaged version.
On a native-size file, the black outline around a character stays a clean hard line no matter how close you look, with no pale fringe beside it. Hair renders as separate strands at the edge of the silhouette rather than as a soft mass. A sky or a wall shows a continuous gradient with no visible steps, even at low brightness in a dark room, which is the hardest test.
If you have never seen that on your own phone, it is worth setting one known-good wallpaper just to calibrate your eye. After that, the bad ones are obvious in a second, and you stop wasting time on files that were never going to work.
The other thing a native file does is survive the crop. Because there is more information than the screen needs, zooming in to reframe costs you nothing. That is why the same picture can be repositioned freely when it is large and falls apart when it is not.
Checking a wallpaper properly before you keep it
Set it, then look at three things on the phone rather than in the gallery.
The edge of the hair, where upscaling shows first. Any large area of one colour, such as a sky or a wall, where banding shows first. And the smallest text or detail in the frame, which tells you whether the file is native size.
Do it at your normal brightness, not at full. Banding in particular is most visible at the low brightness you actually use at night.
Quick answers
Does the iPhone model change how bad it looks?
The larger and denser the display, the more an undersized file has to be stretched, so the same file looks worse on a Pro Max than on a smaller iPhone.
Will the depth effect fix a soft image?
No. It separates the subject from the background, it does not sharpen anything. It can make softness more obvious by putting the subject in front of the clock.
Why does it look fine in Photos but bad as a wallpaper?
Photos displays it fitted to the screen. As a wallpaper it is cropped and filled, which usually means more zoom, and the tilt effect crops slightly further.
Is a live version more likely to look soft?
Often yes, because the video half is compressed more heavily than the still. Judge the still frame, since that is what is on screen most of the time.
Where to get it
Anime Wallpaper 4K – Live stores wallpapers at full size and saves them straight into your Photos library, which removes the two steps, re-download and re-compression, that cause most of this.
One habit fixes most of it: never set a wallpaper you got by screenshotting something.