YouTube works without root. It's just an issue with the proprietary split APK format Google introduced. You have to download the APK manually from a site like apkmirror.
Google creators of the still too open android os.
Edit: The information above is only paritally correct. https://issuetracker.google.com/issues/152120286?pli=1 The issue is that when Google introduced split apks and bundles it did not provide a standard implemention in AOSP leading to fragmentation and proprietary formats by third parties. In the past AOSP could just install apks but these new split APK formats need separate apps to handle them if they are available.