I commented on your suggestion to this on GH. Uploading the artifacts would happen via some SDK before switching to remote execution.
When cloning a task (via WebUI or SDK), a user should have an option to also clone these input artifacts or simply linking to the original. If linking to the original, then if the original task is deleted - it is the user's mistake.

Alternatively, this potentially suggests "Input Datasets" (as we're imitating now), such that they are not tied to the original task. These can also hold references to all tasks that use them, so deleting them would be made harder