Swiss German[1] is a related example for this. Even though Swiss German varieties are mostly unintelligible with Standard German (Hochdeutsch/Standard High German), German writing in Switzerland is mostly done with a variety of Standard German[2]. One of the main causes being, different varieties of Swiss German are so different that it would be difficult choosing a "standard" Swiss German orthography, so a very far variety closer to Standard German is used instead of Swiss German. There are other reasons for this, but this is one of them.

[1] https://en.wikipedia.org/wiki/Swiss_German [2] https://en.wikipedia.org/wiki/Swiss_Standard_German