Strong +1 on both of these.
The current restore workflow is built for the worst case, a full site-down emergency, but the far more common scenario is surgical: find the last clean state, verify it somewhere safe, then decide what to do. Without the ability to push a specific backup to staging, you're essentially flying blind or gambling with production.
The three examples listed here are exactly right and all of them happen regularly in managed hosting. Content deletion with an unknown timestamp, a plugin conflict that doesn't resolve cleanly on rollback, a compromise where you need to test multiple restore points to find where the infection entered. In every one of these, you need to inspect before you restore, and right now Enhance doesn't give you that.
The download limitation compounds this. A backup tool that only exports the current state of the site is just an export tool with extra steps. The value of backups is in the history, and if you can't access that history selectively, the feature is only solving for one narrow scenario.
This would move backups from a break-glass feature to an actual operational tool.