Well, that “local info” isn’t just the artwork, it’s also metadata scraped down in the form of .NFO files in your media folders. If you use a media manager (Ember, MediaElch, etc.), or have previously exported your library, then you should have NFO files in the folders with your media. Kodi generally only reads these files on first import (or a forced “local data” refresh), so if you wish to use these NFO files, then you’ll need to delete your MyVideosXX.db files and re-scan the source. If your source is set to use a scraper, then it should scrape online after the initial NFO scrape.
Removing all sources and re-adding them would possibly fix the problem as well, but may not be as foolproof as just deleting the databases.
Deleting the video database means you’ll lose play states, play counts, etc–they aren’t stored in the NFO files unless your library has been previously exported from Kodi. If they are important to you, installing and doing an initial scan and upload with the Trakt Addon would keep track of 99% of that. That also involves creating a free account on Trakt.com.
One other thing to check is that you don’t have multiple MyVideoXX.db files. Each successive major version of Kodi bumps up the XX number and they’re imported into a new db. These old databases can sometimes hang around and cause issues.