As a linguistic history lover, I really hoped to see a response from one of the amazing pros in this sub.
But as I assume there is no answer coming I researched the topic on my own.
Let me start out and say that many germanic languages still have some form of Wodenstag, named after the germanic God Wodan/Odin. In Dutch it still is woensdag, and in all scandinavian languages (except Icelandic) it is onsdag. And obviously Wednesday also gets its name from Wodan.
So actually high German is one of the few germanic languages that made the change.
But I have to disappoint you if you were hoping for a clear cut answer. As with so many other linguistic questions there is a lot of ambiguity.
And here we also have different theories.
The most common is, that Christian missionaries, disliked the association with pegan gods. So the name changed to Mittwoch. As it was in christian/Jewish day count (Sunday being the first day of the week) the middle of the week.
However this theory poses a huge follow up question. Why then did Donar/Thor (Donnerstag/Thursday) , Freya (Freitag/Friday) and Tyr (Dienstag/Tuesday) got to keep their days?
Some historians point to, that Odin was the germanic high God and therfore it was of higher significance.
Another theory, which I myself think is at least worth considering is that the the change did not come from Christian missionaries from the south but Slavic tribes from the east.
Their day count was of Gothic-Greece influence and here Wednesday is also 'the middle of the week". And all Slavic language continue to this day with this principle.
As you may can see, there is no difinitive answer. But I hope this at least gives some food for thought.
I found a great and well researched paper on the topic from Joachim Grezga on the topic that goes into a l of detail. This is also my primary source for my answer.