This also means that any random person needs to have access to connect to your computer at any given time, meaning holes have to be left in your computer's security system specifically allowing people a route in to access that file. Most people wouldn't want that, nor would they have the patience to manage the ensuing security risks responsibly.
Additionally, since you probably don't have a domain name (whatever.com) attached to your computer, you would have to go by IP address, which for most residential Internet customers changes every time their router restarts. So the link would only be good until the next time you restart your router anyway.