the links are to code that the asker him/her-self created, and chose not to include in the body of the post.
The argument against this practice is that site should be self-contained. Paste bins and picture dumps go down. SO shouldn't be effected by this. Use the features built into the software (built-in image upload and code formatting/hilighting).
Content on SO can be searched on SO. Links to code and images containing text aren't directly searchable. Direct searchability will improve SO's search feature, and might improve google results. The easier it is to find existing questions and answers, the more valuable they become.
Someone might protest: "But the images might be too big or the code too long!"
Then they aren't asking their question correctly.
Good questions that fit the SE format should be succinct and shouldn't require 2MLOC to explain (and usually not even 2HLOC). Code automatically scrolls. The feature was designed to support the style of code that should be placed in the post.
Good questions also shouldn't require large screenshots. They might be helped by a few smaller screenshots that are cropped and shrunk appropriately. Screenshots are often abused when a textual copy/paste is more appropriate.
It seems a lot of people are editing these posts by following the links, grabbing the code/picture, and putting it into the post
People are allowed to edit things on SO. That is explained in the FAQ.
IMO these are worthwhile edits, because they increase the reliability, quality, and prolonged usefulness of SO.