The problem with your question is that it doesn't address the most difficult problem when facing viruses.
Yes, a virus may be a tiny file but it will be buried somewhere in your operating system amongst hundreds of thousands of files. To have that much data be scanned across the internet, you'd have to upload all of it piece by piece.
Where a normal virus scan may take a few hours, an online one would take weeks/months to finish and cost an obscene amount of money in bandwidth to the company providing the scan.
There are some ways to mitigate viruses while they travel across the web:
- Most email providers automatically scan incoming emails for viruses
- Most sites that allow users to upload content scan that content for viruses before making it available to the public.
But the age-old problem with viruses is most of them rely on 'social engineering'. Meaning, if virus writers can get you to download and execute their application (ex. by embedding it in a pirated install of photoshop) on your computer, then there's no hope. Even 'live' virus scanners that sit in the background and constantly scan (like Norton) will occasionally let one through.
The most effective measure to stop viruses from taking over your system is to limit how much of the file system can be accessed by the applications that you run. This is done by setting your user account to not run with 'root' privileges. Meaning, you have to manually type in a root password to access any of the system files. That's what Mac and Linux do and it's the main reason you don't see as many viruses on those platforms.
Sure, there are Mac and Linux viruses but they require a root password each time they want to touch a system file whereas, once a virus gets into windows, it's free game.