We absolutely understand the pain of having "flat" project structure as it is implemented in Salesforce itself - this was one of the first reasons why we have started building The Welkin Suite for our own Salesforce development team.
In The Welkin Suite you can easily create as many folders as you want, with any level of nesting and move files across the folders as you wish. Even more - you can mix different types of files in the same folder (for example put an object, it's layouts and trigger handler class in the same folder).
And as you have mentioned about sharing this structure with your team members - this is also implemented in TWS, however in a bit different way. When you create a project in TWS you can enable "Project structure synchronization" which will create a Static Resource on your organization with project structure information. Each time something is changed in the project structure locally - this change will be uploaded to the org immediately. At the same time your team members will get the same project structure next time they create a project from the same organization or next time they pull project from the org.
For some more information on how this works you can read an article in our blog Using custom Salesforce project structure to boost productivity, take a quick demo on YouTube Customizable Salesforce Projects Structure in The Welkin Suite and read our documentation about Project Structure Synchronization.
Hope this helps.
Looking forward hearing back your feedback on this features!