This is a false anecdotal dichotomy: either install latex on your computer at the cost of "clogging up your filesystem" (whatever that means), or give up your freedoms.
textlive-most (which is a meta package which includes almost everything an ordinary user need) uses 1.2GBs on Arch Linux, so for sure it's not "couple of GBs". And even if it takes a couple of GBs: I'm using ~60GBs in my root filesystem, and never experienced any "clogging" (granted, GNU/Linux doesn't use Windows Registry).
If installing programs "clogs up your file system" in Apple's proprietary fork of BSD (don't know/care how they call/stylize it these days), another viable option, before throwing away your freedoms, is to consider switching to a different filesystem or operating system which doesn't "clog up" when you install new programs (and which isn't riddled with backdoors and doesn't spy on you, like Apple products do: https://www.gnu.org/proprietary/malware-apple.en.html https://www.gnu.org/proprietary/proprietary-surveillance.en.... ). Now I'm not sure whether this is an issue with HFS+ or a more general one within Darwin, but what is the point of having harddisks with large capacities (measured in TB these days) if you can't actually use it?
> ShareLaTeX is that I can use LaTeX from any computer (connected to the Internet) to access any of my automatically synchronized files and have an automatically updated install of LaTeX. I personally found that value proposition worthwhile.
I'm not seeing any convincing arguments or any "worthwhile propositions" here. With GNU/* and *BSD, that burden is on the package maintainers. System updates do include latex updates too (I know that it isn't the case with proprietary system you're using, but that's an argument for switching to a free/libre OS, not throwing away your freedoms). And I am able to synchronize my files (including .tex files) files across devices over the internet using syncthing, while still not yielding my rights and data to others, and there are plenty of FOSS alternatives to syncthing too.
And even if your original dichotomy was a real dichotomy, I would encourage people to protect their freedoms, not to throw it away for convenience.