Changing existing date time field
Unfortunately, as suggested, programmatically changing the config won't work, as all dates will show empty. Which explains why it's locked in the UI.
You'll need to browse your DB and find the node__{field_date} table and manually remove the time part for all values.

Then make a sql export of this table.
Repeat the above with node_revision__{field_date}.
In Drupal, manage fields, delete your field_date. Recreate field_date with Date only. Import your sql db table exports you had made.
Flush cache in Drupal.