From what I understand, but I'm not an expert, the benefits are mainly:
1. Controlling the printer from a remote location.
2. Monitoring the printer from a remote location. (As mentioned above)
3. Transferring print files to the 3D printer over LAN (instead of being tethered to the slicing machine, or transferring via SD card)
4. Changing the printer settings using a web interface (wireless), instead of the control knob on the printer itself. (More or less a specific section of #1)
I had heard many people reference using a Pi which their 3D printer, and didn't understand for what purposes. dkj4linux was the first one I saw using a Pi, in this fashion, and he loves his, and I learned the basics benefits from his posts and photos. I did more reading about it, and see where it can benefit some people and their setup or needs. There's lots of YouTube vids showing various options, and setups. But all of them have the same basics.
For some people it's a huge benefit, for others, they did it because they could, or wanted to prove they could, but didn't truly gain a lot. Personally I haven't decided for me if this is the path I wish to take or not. I believe it's all a personal preference, and most of it fits into the "nice to have" category. With that said, the main benefit I see for me, is the transferring of the files. The others "options" would be because I could, once I solved the transferring of files problem, instead of moving a SD card back and forth, being I've elected to not have mine tethered. I did elect to have my printer in the room that I am in the most. Some people want their's in a basement, and don't want to have to go "downstairs" periodically to check on the print.
But again, I believe there is no correct answer, as much of what benefits can be gained, by choices people have made to how/where they plan on using the printer.
I hope this helps some (being I didn't provide any links).