DSC-Resource: How can I delete a registry key (not value)?

This is now possible, see VertigoRay's answer.

This isn't possible at the moment with the Registry resource, as you've discovered.

You can use a Script resource or write a full custom resource instead.

This is possible, as documented:

To add or remove a registry key, specify [ValueName] as an empty string without specifying ValueType or ValueData.

Example

Registry ConfigureRegistry
{
    Ensure    = 'Absent'
    Key       = 'HKEY_LOCAL_MACHINE\SOFTWARE\SomeKey'
    ValueName = ''
}

PSDrives also work:

Registry ConfigureRegistry
{
    Ensure    = 'Absent'
    Key       = 'HKLM:\SOFTWARE\SomeKey'
    ValueName = ''
}