Create new Apple ID solely linked to new @icloud.com email?
It does not seem possible to create an iCloud-only Apple ID after the fact.
However, you can create such an Apple ID during the initial setup process of an iOS device or macOS user account.
Create an Apple ID when you set up your device
- Tap Use your current email address, or tap Get a free iCloud email address.
https://support.apple.com/en-us/HT204316
I've confirmed that this works from both iOS and macOS. Wipe an iOS device or create a new macOS user account and you will be allowed to create a new @icloud.com address rather than provide a 3rd party email address.
Each Apple device additionally seems to have a strict limit for the total number of iCloud Apple IDs it can create: Why won't my secondhand iPad let me activate an Apple ID?