Teamsite without subsites

Deleted, while I am a user of subsites in specific situations, I would encourage you to consider this: if you intend to grant each department control of their subsite and they adopt SharePoint well, that they all exist under one site collection to begin with will limit what they are able to do and may prevent them from "growing" their SharePoint environment because they are restricted to the rules of that site collection.

While this is not necessarily a bad thing for an organization learning how to use SharePoint (less of a functionality flood), it does present a situation where your power users are running into walls almost immediately that wouldn't be there if they did have a site collection available to them. For example, handling external users--if any one of your departments sees a need to allow external users and another sees a need to completely prevent external access, resolving those requirements and enforcing those security needs in one site collection is far more difficult (and may actually be impossible, would require creating very specific security roles at best) than setting up multiple site collections. Navigation is another limiting factor--if there are two competing visions of how navigation should be at the "global" level, somebody loses that battle when they might not if they had their own site collection.