macOS shouldn't typically ask for Touch ID or password confirmation simply for copying files to the Desktop, as this is a regular file operation that doesn't normally require elevated permissions, especially if you're working within your user directory.
However, there are some possibilities as to why it may happen:
If you have additional security settings enabled through third-party security software or enterprise management policies, it may restrict standard file operations and prompting for confirmation. In this case, you can disable the security setting to resolve the issue.
Since the problem only occurs on your desktop, it may have permission issues. You can right-click your Desktop folder, and select "Get Info" to check its permission settings. If everything is fine, your account should have read & write access to your Desktop folder.
Another reason for the issue that macOS keeps asking for Touch ID permission is bugs on your current operating system. If you find a new update available, you can update your Mac to fix the problem.
If the issue persists, you can disable Touch ID on your Mac or create a new account and test if you can copy files to the desktop without macOS prompting for Touch ID permission.