Thanks for bringing this up. Setting the CESIUM_BASE_URL is necessary if you’re importing CesiumJS as an ES6 module. Matt explains it a bit here:
If you are just copying the Build folder and including Cesium.js, then you don’t need to set it because we can find it automatically. We look for the location of Cesium.js script in the HTML and create a relative path from that. If you are building an app from modules, then there is no relation to where the Workers, etc… live on your server vs where your compiled JS lives, that’s when it needs to be set. It just so happens that in most modern tooling setups, this is the case.
From this GitHub issue: https://github.com/AnalyticalGraphicsInc/cesium/pull/8314#issuecomment-546487096
Although, if it fails to detect the correct base URL it should throw an error, I think. Can you describe your setup and how you’re loading in the library?