@MushroomUm, no.
Back in the day when men were men, PCs ran DOS, and we were reading Usenet on 80x25 text-mode screens, this may have been true, but it hasn't been in 20, 25 years at least. I mean, you'll still see it sometimes in terminal-mode stuff like Unix man pages, or stuff that was created as a flat text file and just wrapped in a modern format wrapper, but anything in any remotely modern format is not adding actual characters to the text; it's adjusting word spacing to pixel-level precision on the fly as it flows the text.
(Adding actual space characters to anything HTML-based β and practically everything is HTML-based under the hood these days β doesn't even do anything, because HTML collapses whitespace.)
The reason full justification on narrow columns so often looks crappy isn't because the system can't or isn't doing fine adjusting of word spacing. It's just because when you've got unbreakable chunks of text that are relatively long compared to the space they have to fit in, you'll frequently have situations where you've got a long word coming up next and not quite enough space to fit it on the current line, so there's a lot of whitespace left over on your current line that you've got to do something with. So you end up with a line that has a short word on the left margin and a short word on the right margin, with an unreasonably wide gap between them, and then a long word by itself on the next line.
But the thing is, it doesn't look a lot better left-justified. You just end up with your unreasonably wide whitespace on the right margin instead of between the words. It's not really full-justification problems; it's just narrow-column problems.
Hyphenation lets you avoid this situation by breaking that long word and putting part of it on the line with the short words. But then you run into the problems that browsers are often not very good at auto-hyphenation, and if you don't actually control the formatting of where you're putting your writing, you probably can't tinker with the hyphenation settings anyway.
I've been working recently on a bunch of pages that have photos and diagrams floated right so the text flows around them on the left side, and I've been running into problems because they work fine on my high-resolution laptop display, but on my tablet the gap between the left side of the image and the left margin of the page is often very narrow to non-existent. So I end up with places where I have one word next to the top corner of the image, and then the next word, which is just a bit too long for the space, is way down on the line below the image. Changing justification settings does absolutely nothing to address this. Turning on hyphenation does, because it lets you break that word that's too long for the available space and fit it in in pieces.