...but it is probably not wrong to assume that the "computer being on" also implies an endless connection to the "world-wide-web" where, every type of nastiness resides, relentlessly seeking entrance into the inner sanctum of your essence.
In my case it's wrong
I'm "paranoid" too: the main user account I use for accessing the Web is... living entirely in ram! It's created by a tiny script which sets up a temporary user directory in ram and copies the web browser into that temp directory. All it takes is one command to kill the current browser, delete that entire user dir and re-create it, copy the browser (locally, to that user dir) and then launch that browser. A security exploit would need to first exploit a security hole in the browser and then manage to escalate privileges to be able to compromise my "real" users accounts. It's not impossible but I'm not losing sleep over it.
That and my ethernet switch is, on purpose, near my desk so I can turn the switch's power off when I go to sleep (being paranoid my workstation has, of course, no WiFi capabilities).
That said I realize it's definitely not the norm to run a browser in a throwaway user account living in ram
Now, as a developer using my computer as a tool to make a living, the one thing that pisses me off the most is when it crashes. It's not that I "need" six months of uptime for my workstation: it's that the fact that my workstation can trivially reach six months of uptime is quite a hint that the system is rock stable solid.
The other benefit is that by running Debian Linux on my workstation and seeing how stable that thing is, I gives me confidence that my servers running Debian Linux are stable too.
So I can work and be quite confident that, baring any hardware issue, my computers will simply do their duty without making me lose my time with crashes / reboot / unstable behavior