Getting artwork to show on music added to a computer system depends on how and in what way the music was added to the system. If you simply bought the physical CD, you should use a music import program such as WMP or iTunes that can get that releases artwork and add it to each track off the release when the content is imported to your computer system. If you purchased the digital music files from like amazon, or even iTunes, the music files should already be embedded with the original release artwork already, and when the Spotify app is pointed to the folder or location of where the music files on your system is stored at, the Spotify app should pick up the artwork when the content is played.
Can you list what OS, and devices this is happening with with regards to the artwork not showing with local music files in the Spotify app? Also can you list what Spotify app versions this is also happening with?
Do you know what program you used to import the music files with when adding to your computer system, if the music files came from a physical CD release? Or if you purchased the digital music files which service did you use?
If you used the Spotify desktop app to import your local music files with, you might toggle off all music import sources from in Settings ----> Local Files, log out of the Spotify app, log back into the Spotify app, and then toggle back on the music locations your music files are stored at, and then try again to see if the artwork will show correctly when played, after the Spotify app finishes adding the local music files back again.