Puede usar esta consulta DELETE, que es genérica y se puede adaptar fácilmente para admitir más campos:
DELETE tablename.*
FROM
tablename LEFT JOIN (
SELECT MIN(id) min_id
FROM
tablename t INNER JOIN (
SELECT
emails, MAX((name IS NOT NULL) + (surname IS NOT NULL)) max_non_nulls
FROM
tablename
GROUP BY
emails) m
ON t.emails=m.emails
AND ((t.name IS NOT NULL) + (t.surname IS NOT NULL))=m.max_non_nulls
GROUP BY
t.emails) ids
ON tablename.id=ids.min_id
WHERE
ids.min_id IS NULL
Consulte fiddle aquí .
Esta consulta devuelve el número máximo de campos no nulos para cada correo electrónico:
SELECT
emails,
MAX((name IS NOT NULL) + (surname IS NOT NULL)) max_non_nulls
FROM
tablename
GROUP BY
emails
Luego me uniré a esta consulta con tablename, para obtener la ID mínima para cada correo electrónico que tenga la cantidad máxima de campos no nulos:
SELECT MIN(id) min_id
FROM
tablename t INNER JOIN (
SELECT
emails, MAX((name IS NOT NULL) + (surname IS NOT NULL)) max_non_nulls
FROM
tablename
GROUP BY
emails) m
ON t.emails=m.emails
AND ((t.name IS NOT NULL) + (t.surname IS NOT NULL))=m.max_non_nulls
GROUP BY
t.emails
y luego elimino todas las filas que tienen un ID que no devuelve esta consulta.