I print a lot of images. Many are made as silver gelatin prints in the darkroom and many others printed digitally from scans.
One thing I have noticed, when you hand someone a print to look at they really look. It doesn't seem to matter if it is a large framed print, an 8x10" on the wall, or a pack of 5x7s, people tend to take their time and look deeply into the print. Compare that to the way people speed scroll through online galleries, like Instagram and such. Images have to really stick out at thumbnail size for people to click on them. Quite often the thumbnails that do catch the eye are the over-saturated, over-sharpened, over-processed images that you see so much of these days.
Of course, there are other reasons to print photos other than for showing...
Your digital files will be lost
You may have a copy of every file on a hard drive, and a backup copy on a separate hard drive, and another copy in cloud storage... Great, your files are secure - for now. At some point in the future the RAW and JPEG file formats will become obsolete. Remember Super 8, VHS, BETA, 5.25 and 3.5 inch floppy drives, zip disks, 8 track, 1/4 inch tape, 1/2 inch tape, need I go on? Yes, you will probably be able to convert your files over to whatever the new format is but, at the rate many digital photographers shoot, that could be hundreds of thousands (millions?) of files.
Eventually all of us will shuffle off this mortal coil and we can do so confident that no one will get past our encrypted password. Those digital files will live on, unseen, until someone throws your back up drives into their wheelie bin.
Prints (and negatives) will be around indefinitely if stored reasonably well. I have photographs of my grandparents wedding and some of my mother as a little girl in the 1940s. These are irreplaceable. Do you think that many digital images will survive the next 70, 80, 150 years?
Printing can improve your photography
Most photos are viewed on a screen these days and how they look will vary from screen to screen. When you view a print your mistakes will be more obvious. Whether those mistakes are in composition, exposure, or processing. Learning from those mistakes will help you improve.
It's your art
Nothing feels better than holding one of your own prints in your hands. Okay, there are things that feel better but, hyperbole aside, it's still an awesome feeling. Prints of your own work make great home decor items. If it's a good print, print it large and hang it on a wall. It doesn't matter whether you choose a canvas, or metal, or an expensive custom frame, you will get more enjoyment from your photos by putting them on display.
Photographic prints are real things, tangible things that complete the process of making a photograph. There really is nothing else that can take you back to a special place or time like an actual photograph.
It isn't a photo until it is printed
I've set up a kind of gallery in my darkroom with prints hanging on three of the walls. Nothing fancy but enough to display a couple of dozen prints at a time.
When I make a new print, and I deem it "wall worthy", I'll cut a mat for it and attach it with lead-free tape. I bought some self-adhesive hooks that can easily be removed without damaging the wall or the paint and hang the prints using small clips. It is a cheap and simple solution that makes it very easy for me to swap the prints over every now and again.
Many ways to print
There are many different ways to print photos, from large scale wall hangings, framed prints, photo books, individual prints and there are just as many different print media from which to choose - all kinds of paper and paper surfaces, canvas, metal, glass, etc. Even those 15¢ 6x4" prints from Woolies or Officeworks are worth having.
You certainly don't need to print everything, that wouldn't be remotely practical, but do consider printing your best work.
One idea you might like is to make an annual photo book. Pick your best 20-30 shots each year and make them into a book, in time you will be glad you did.