Are you looking at the prints with a microscope or on the wall at normal viewing distances? The numbers all seem to be overkill here.
It may have changed but there's people on Lula who have forgotten more than I'll ever learn, but from what I remember and have been told the "effective" res on most inkjet printers is the equivalent of a 60-90 LPI halftone but the "microwaving" and other tech makes it appear much better than reality.
Regarding printing an image sent at those high dpi sizes, 360, 720, etc. Files with that density seem way on the high side. Usually, 300 dpi as a general rule of thumb will suffice for nearly all inkjet printers for most substrates. However, for many images that can be just a starting point.
Do an experiment for your self. Take a file sized your normal print size and print it as is and able on the back the details. Now take that file and size it for your print at 720 dpi, another at 360 dpi, another at 300 dpi, 240 dpi, 180 dpi, 150 dpi, even 100 dpi. Print them all and notice both the time it takes to send to your printer, complete the printing cycle, the file sizes, etc. Mark the res/file size on the back.
When all the prints are in hand, put them on a table or on the wall after shuffling them all. No fair peeking at the back! take a look at normal viewing distances and have others do the same. More than likely, very few will be able to tell the difference between each print let alone be able to take each print from lowest-to-highest file dpi and put it in order. On the wall at normal viewing distances even the lowest dpi input you'll probably pick out, maybe the next lowest and then it will become more difficult.
When you print onto canvas, each file will probably be even harder to distinguish from one-another due to the weave of the material. Canvas is very, very forgiving of the input resolution I've found.
The math will tell you one thing, the print on the wall tells you another and if you push the envelope and ignore the numbers you may be quite surprised!
I'll share with you a couple examples, one from the mid 1990s outdoor advertising campaign and a more recent from a museum show I produced a few year ago.
The 1990s image started as a 35mm negative that was scanned as by a Kodak Pro PhotoCD lab at 6000x4000 pixels. The composition wasn't wide enough so the image was cloned for the format which got us our aspect ratio of 24:7. Seems like a weird size... However at the time, it took a lot of patience to make this thing work. The file got sent to the billboard company and they printed it. 48x14 was the largest of the billboard size signs they produced. I drove by it on the freeway about 50-60 dpi and that image looked great!
More recently my colleague who is a wiz with any camera he's handed had some lovely work shot with his iPhone. The two of use took on the challenge to photograph several California Missions for a prominent museum for a few years since they had nothing scheduled and needed to fill the space. Though many of the photos were originally shot with 10-12mp up to 36mp images and most of the prints delivered were nominally 16x24 prints, we still needed some large images to enhance the show's design. Several of the images we chose were taken with his iPhone. With good craft not only did they print well at the 16x24 inch size which made most of the show uniform in size (making it easy to frame and hang), but we took those same iPhone images and printed them up to 24x36 (the math stops most to a print of 10x12) and placed side-by-side with the rest, looked great. We took both the Executive Director and Curator on a walk-through after the show was hung and before the opening to discuss our work. When we were finished and pointed out the photos that were shot with the iPhone (probably a 4), they were both blown away! We did the work ourselves simply using Photoshop and printed them on my Epson 9900.
Since those shows and even before, I've taken many images that the math tells me to stop at some piddling print size and set aside the math, pushing how far I could blow-up the image while ignoring the math. You may be quite surprised at how large and how nice your image will look once you print it and hang it on the wall.
Bottom line, don't let the file resolution and the calculations get in the way of a good and large print with these wonderful printers. Push yourself out of the box and see how far you can go!
