Stack Overflow Tag Usage
This TagName column holding all the tags is denormalized and the non-equi-join ON #MyPosts._tags LIKE '%&lt;'+Tags.TagName +'&gt;%' kills performance. There's no efficient way for the optimizer to do this join, thus it's like a Cross-Join to the 50000+ rows in Tags. 

But the base data model is normalized, there's an associative table PostTags between Posts and Tags and then it's simple equi-joins:

with MyPosts as 
 (
-- The tags and scores of my posts
   SELECT
     Question.Id AS PostId,
     Answers.Score
   FROM
     Posts as Answers
   INNER JOIN
     Posts AS Question
   ON
     Question.Id = Answers.ParentId
   WHERE
     Answers.PostTypeId = 2 AND
     Answers.OwnerUserId = ##UserId:int?8041461##
 )
-- All of the tags with the total score and the amount of times used
SELECT
  t.TagName,
  sum(score) as "Total Score",
  count(*) as "Answer Count",
  cast(sum(score) as FLOAT) / count(*) as 'Average Score'
FROM 
  MyPosts AS p
JOIN PostTags AS pt
  ON p.PostId = pt.PostId
JOIN Tags AS t
 ON pt.TagId = t.Id
GROUP BY t.Id,t.TagName
ORDER BY "Total Score" DESC;


Your HAVING sum(score) IS NULL is not needed, there's no NULL score.

See SEDE query which runs fine with John Skeet, too :-)