> You need to crop, color correct, distortion correct, noise correct, exposure correct. Only after that would you ever really want to apply some kind of bokeh filter.

Modern phones already do all that - and seemingly in that order.

As a photographer, what I find lacking are the lenses. You can only squeeze so much light from the relatively tiny lenses. Perfect recent example was kids Christmas play. Sitting back 25+ meters, with somewhat dim lighting and fast moving kids, I could see the other parents with their smartphones and tablets getting very poor photo's and vids - whereas my Nikon had zoom galore and excellent clear focus.

Physics matters.

I've never seen any phone get even half as good results as any DLSR released this decade. Just because the phone software can do it doesn't mean it's any good. I mean my phone has photoshop on it. That's pretty good, but nothing beats a proper suite of tools on a color calibrated monitor.

Modern phones do not automatically crop, to my knowledge. They do attempt to color correct, but they don't always get the correct colors. (There needs to be a reference to infer the appropriate white balance, and such is not always available.)

It's not the software that holds back phone cameras. It's the literal size and shape of the sensors and lens.

You can already shoot RAW on a phone, but putting Photoshop on the phone won't solve the lack of depth of field inherent to the lens and sensor setup.

Does the RAW format save the kind of information that the software uses to guess at bokeh (depth sensors, multiple lenses, multiple shots, defocused pixels)? Or is there some other format that could save all that info, so you could really use the phone but do the processing later?

There’s no, but there isn’t really a need. The R package mentioned in a comment in this thread achieves a similar effect using no additional data.

Ray tracing will suffice!

It shows a hand made depth map. You can't just 'raytrace' a 2D image and magically add depth of field.

You can shoot in raw on most high end smartphones now if you want to do handle that after the fact, but the default used by the camera software does all of that