Several years ago, there was a discussion suggesting the enforcement of uploading images rather than embedding them from third-party URLs.

It's a very important feature because images hosted on third-party URLs often become unavailable, making many topics immediately less useful.

With this feature, every time a user pastes a URL to an image hosted on an external website, it should be uploaded and embedded as an attachment, rather than relying on unreliable third-party URLs.

However, it appears this feature has not yet been implemented. So, I hope this will be implemented in the future.

Actually, it was already available for some time, so http image calls on https pages wouldn’t break the SSL delivery. This was solved by importing all these images as attachments. But it was removed again after some transition period. 

Personally, I would love to see this feature with a white-list option. People often link community-related images from a few known sites in our field, which we absolutely don’t want to loose, but certainly will at some point in the future. Picking these sites for an automatic import would be great. 
Importing every linked media can easily lead to legal troubles (and significant fines), when the content is copyrighted, as it usually is. 

8 minutes ago, opentype said:

Actually, it was already available for some time, so http image calls on https pages wouldn’t break the SSL delivery.

As I recall, it was proxying, not uploading, so it wasn't as reliable as uploading and quite overengineered. Immediate one-time uploading from third-party URLs is much simpler and much more robust than proxying them all the time.