If the OP was actually concerned with finding a solution to their problem (which is absolutely an edge case) and not just being a squeaky wheel, they'd pay $30 for InSync or find another free tool that syncs with Google Drive. The Google app is a bonus provided by Google to make the use of their service easier. The OP complaining about being a paying customer is pointless because what they're paying for is still completely useable.
There is no way to sync a device without an app. The app is not a bonus, it is a core feature of the service.
You just assert this as if it was self-evident, but it's not. The same feature can be offered for free and as a paid component of a package, just like the same code can be licensed to some under the GPL and to others under a proprietary license.
In this case, syncing is part of the service being purchased, and the means to achieve that is absolutely part of the package, even if it's also offered for free to others.