Understanding the given correlated subquery

According to this answer:

This is a known problem in MySQL. Rumors say it will be fixed.

The problem is due to a missing optimization when a subquery using IN is incorrectly indentified as dependent subquery instead of an independent subquery.

This causes the subquery to be run a huge number of times, which is unnecessary.

I'm not sure why you need to join all three tables every time. For your specific example, what about the following query:

WITH rel AS (
  SELECT prm.power_relation_id
  FROM power_relation_members prm
  JOIN power_lines pl ON prm.member_id = pl.id
  WHERE pl.geom = :BIND_VAR_HERE -- in this case, 'abc'
  GROUP BY prm.power_relation_id
) SELECT
  pl.id, pl.geom
FROM power_relation_members prm
JOIN rel r ON prm.power_relation_id = r.power_relation_id
JOIN power_lines pl on prm.member_id = pl.id;

You reference member_type and power_relation_members.id in your SQL, but nowhere are they mentioned in your post apart from the DDL.. Is this important logically, or just a filter?