Shop is relatively new compared to the desktop version, so that’s probably the why. FI, I don’t understand why there isn’t a ‘Save as’ in Shop. It’s under constant development, and features being added on almost a monthly base.
If you upgraded your participants to Pro subscription, they might as well invest some time in the workings of the desktop-version and profit from the difference between Web-based Shop and Desktop Pro. One of them being the use of extensions and in your case the Trimble Connect Extension specifically, which get’s installed as a ‘native’ extension, so everybody has it.
In the link above, there is a little tutorial for setting up commonly used libraries in the desktop version, but here it is again:
Still, some questions, can or may the participants alter the blocks?
For modeling you don’t need to use the download option of the files and then open the downloaded file in SketchUp, instead, you can use the extension to open a model and publish it. Or use [menu]File->Trimble Connect.
Then, they cannot ‘Save’ the file (error: other application has altered it) and they would need to publish it by using the extension, instead. This way, all the alterations and version history is kept in the cloud (who modified it when)
It all depends if they are allowed to change the components of the (former) Warehouse Collection and how often they change. With the tutorial link, the Trimble Connect Sync apps keep you all on the same page.