Whereas the Podcast App displays the image which shows in the iTunes Store (and which is referenced in the feed) the Music app evidently only displays images actually embedded in the file. The Monstercat Podcast has such an image embedded in its top file; the Ear Biscuits podcast does not, and I assume you will find that to be true of the others you complain of.
You can check the status of this by subscribing in iTunes on your computer. When you play an episode in a podcast you have subscribed to the image will show next to the progress bar at the top of the window. If you command-click on this (Mac, or control-click on Windows) you will see a larger version of the image. You will see that Ear Biscuits has no such image.
The inclusion or non-inclusion of these images is entirely up to the author of the podcast. However I suppose if you really want to take the time and effort you could copy out the podcast image from the Store page, and then embed it in every episode of the offending podcasts: you would do this in iTunes on your computer using the method detailed in this page:
http://wilmut.uk/coverart