You can capture great photos with today's phones, and there is software out there to spruce the photos up a bit, too. I've seen professionals out on shoots with iPhones, because they can get that moment and don't need a 5D MK IV (what I have).
However, if you want to do a portrait, for instance, you're never going to get to the quality of a full-frame digital camera without some nice glass to go on top of it. With that kind of equipment, you can zoom into the eye and see what kind of lighting was used, detail that a cell phone won't ever be able to capture.
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You also have depth of field issues with cell phones. You may be able to snap a rapid succession of photos (like 30 or whatever your phone supports) and blur layers to make it appear like there's depth, but you can also do that by slapping a f/1.4 lens on a camera and calling it a day, too.
If you're interested in photography, go for it with a phone. Work your way into a used crop sensor with better glass, and then if you want to be a pro, get pro gear as it will cut your time down drastically with post-edits.