Not sure about cover arts. For sidecars, they are called sidecars for a reason. What purpose does it serve to save a sidecar file in a central location? Might you as well just turn off sidecar writing?
What purpose does it serve to keep them next to the video files; that can't be said of keeping them in a central location? Why would you equate separating them from video files to not having them at all. I like that they exist, and keep my tagging information, so my MC experience is better. I would not want to go without them, that would make MC much less useful. I just don't want to see them cluttering up my folders.
For me, I keep videos in a folder called Videos. (I keep music in a folder called Music, and pictures in a folder called Pictures) I do this to keep my media types separate. When I look in the video folder, I want to see video files, not other types of files. It not only doesn't help me to have non-video files in the video folder, it makes it far more difficult to find and assess what videos i have when i have to scroll through all the extraneous non-video files. I end up with 3 files for every 1 video. That causes me to have to scroll far more often that should be necessary when browsing files outside of MC.
Keeping non-video files out of the video folder also makes auto-import easier, as I don't have to choose what file types to include or exclude in the Video (or Music or Pictures or Documents) folder(s). Also, if I'm tagging lots of tiles, and I happen to make 2 changes to tags before the first change is written, MC can see that as applying to a separate file, and I often end up with sidecarfilename(1) as an orphan file, and often as the only file left in a folder where the tagging has moved the file I actually care about, and the delete empty folder after moving doesn't work, because the folder isn't empty.
I propose a better question would be,
What purpose does it serve to save a sidecar file next to the video file? Why is that ok for video files, but not okay for Audio files, which is how MC has operated since forever. That works great. If I want to analyze/deal with cover art (or video series and season artwork), I go to the designated folder for cover art. The fact that MC only keeps series and season art for video files here, but not other art for videos has often confused me. I don't see any benefit to filling my VIDEO folder with non-video items. It just feels wrong, and makes my life more difficult than it needs to be, for no benefit that I can see.
I would also argue that keeping non-audio files with audio files is also wrong, and the associated pdfs and other non-cover art for audio should also be stored in the central location, but that is for another day.