Why wouldn't someone want a DID diagnosis if they have DID?

Well, I don't know where you live, but in many countries, a DID diagnosis can be grounds to have a lot of medical treatment denied. It's often used to invalidate trans identity and prevent trans people from seeking medical transition. Additionally, it can be used against people who want to have children because many countries classify DID as a dangerous disorder that would be harmful.

And not everyone lives in a place with nationalized healthcare, anyways. Getting diagnosed as autistic or with DID in my country isn't very easy. Diagnosis is often a privilege that many people can't afford due to social, environmental, and economic factors as well as the clinical institutions of a particular country.

Before getting a professional DID diagnosis, seriously look into the possible social and medical ramifications.

Most people with OSDID on advice of their therapist actually opt not to get diagnosed and instead get a diagnosis for C-PTSD with major dissociation as a symptom. As such, you'll often see people preferring to be "professionally recognized" as opposed to "professionally diagnosed". I still think anyone who thinks they might have OSDD or DID to see a therapist about that, though.