As I have pointed out some time ago, if people want to contribute mathematical content, they should post an answer, not comments.
In this specific case, @Nate Eldredge and @Michael Greinecker should have posted their content in answers.
Comments are (1) ephemeral and meant to be deleted, and (2) should be used mainly to suggest improvements to the question, not answers or partial answers. The moderators did nothing wrong if they removed them or moved them to the chat, because they were not supposed to be there in the first place. SE is working as intended here; users just need to stop using it in the wrong way. :)