This script works fine:

DELIMITER $$

FOR i IN 1..3 DO

  SELECT i;

END FOR;

$$

DELIMITER ;

This script returns an error:

DELIMITER $$

FOR system_time IN 1..3 DO

  SELECT system_time;

END FOR;

$$

DELIMITER ;

ERROR 1064 (42000): You have an error in your SQL syntax...near 'system_time IN 1..3 DO

Looks wrong. It should work like the first script.
FOR SYSTEM_TIME should have a special meaning only in certain contexts.
In a FOR loop, SYSTEM_TIME should be treated like a normal index variable.