Why it is better than offline editor (like TeXnicCenter) and code repository (like Git)?
Although most users of LaTeX are in the STEM fields, they're also way too busy with actual research to find joy in dicking around with command-line tools.
I think the computer field is unusual in that computer people think everyone must be dying to learn The Way even if it costs them time and (from their perspective at least) risks significant losses. Doctors advise diet and exercise, but don't find it puzzling when people don't.
Even more importantly, setting up and maintaining a latex installation may not be a lot of time, but if you don't have much time, it becomes a bigger fraction of it. It's a big activation energy to get over if you don't have a lot of energy.
If you are writing papers regularly, then you may find it worth it, or easy to invest in your own setup. If you aren't, it is a lot to manage.
Also they support collaborative editing and adding editor notes to a document.
It's significantly easier to do collaborative editing of latex files with such a web service. But even a single person might want to use them, because maintaining latex dependencies can be bothersome.
It can be a lift to get non-computer-savvy folks to use a highly-managed system like ShareLatex (which is a great system). But it would be impossible (not merely difficult) to do so if "just use git for collaboration" is your message!
If a lot of your documents are collaborative, this turns out to be a major factor. (For my personal work, I'm happy to use Emacs and TeXshop and keep all files resident on my laptop.)
I recently typeset a (stunning looking) master thesis for a friend and she was able to edit the text while I dealt with formatting, setting stuff up, etc. (Well for that project, also big props to pandoc [1], as it easily converted docx to tex including footnotes!)
Otherwise it's nice, because I set up shared projects with good looking CVs for some non-tech friends and even a template to write nice looking letters/invoices and they know what to change and how and I could hide most of the stuff going on in template files.
[1]: http://pandoc.org/
LaTeX is from the 80s. I understand it has grown over time, but to >1GB? That's huge, even for modern standards, for just a typesetting program. The documentation is a dependency that seems to be forced on you (it's not an optional dependency in Debian), and fonts are also big. But even without that, you're left with about 600MB if I recall correctly which is still huge for just formatting text right?
I am quite happy to dedicate 1GB to that. Especially in a world, where random websites tend to dump 3-4MB on me (with liberal use of adblockers) to render a few paragraphs of text.