Add the Send a Copy feature to the desktop/online apps too
In Teams mobile app you can tap the ellipsis for a shared file and then tap Send a Copy. This sends the file as an email attachment in Outlook (no downloading necessary). This functionality needs to be available in Teams online/desktop apps.
To share a file from desktop/online you have to first download and then toggle to Outlook to start a new message. I'm trying to implement Teams across my organization but for users who work in Outlook all day, all the extra steps to get a file from Teams (SharePoint) to Outlook is click intensive vs. sending attachments from the mobile app.
Note: this is for sending files to external recipients who don't have access to our Teams/SharePoint environment.