This problem definitely isn't as common as png overkill, but I think it should be addressed in some way.
A prime example of jpeg overkill would be this pool:
http://danbooru.donmai.us/pool/show/974
The first image in the pool, a 2.3 megabyte jpeg, can be saved as a 300 kilobyte png. Another example would be post #616416, where saving the image as png reduces filesize by nearly 50%.
There's no reason to upload the smaller png at this point, so this thread is about future posts involving such images.
A lot of grayscale images can be smaller when saved as png, even if the original had jpeg artifacts. I think that users uploading black and white comics and similar images should be encouraged to check to see if the image is actually smaller as png. It takes a small amount of time to do and it could help reduce some of the strain on the servers.
I suppose a problem with this could be that the source is a jpeg while the image itself is a png, but that doesn't seem like a huge deal to me. I'm also not sure if it would affect the image duplicate checker.
Updated by 0xCCBA696