I hear what you're saying, but I think you're still painting an inaccurate picture. Virus scanners are meant to detect known viruses that can sneak onto your computer without you knowing. An app can't connect to Google Drive without you knowing. You have to actively connect it. Mentioning a firewall is irrelevant for the same reasons.
Imagine, for a moment, that the coders who programmed your web browser put code in it that waits until 2/14/2013 and, after that date, shows you nothing but pictures of cats when you browse the web. There's no firewall or virus protection software that's going to save you from that. After all, it's not a virus. It's just a web browser that favors cats.
I suppose, if you're using Chrome, you could make the argument that it's open source and that the community of developers would catch this silliness before it is distributed, but unless you're downloading the source code of Chromium and compiling it yourself, there are still ways or these types of things to slip through.
That aside, your web browser has access to your entire hard drive right now. Not just the files needed for web browsing, and not just its own files... your web browser currently has access to your entire system. It didn't ask for permission. Any software installed on a computer has access to the whole system. Compare this to connecting web apps to Google Drive, there are various restrictions that can be placed on these apps. Upon connecting the apps, it tells you what access these apps need. If an app starts doing bad things to a bunch of users, Google also has the ability to nuke this app's connection for all users.
I'm not saying that connecting an app to Google Drive is 100% safe, but I think you're under the impression that installing software on the computer is somehow safer. It isn't. Not even with a firewall or anti-virus protection.