> never really understood how just adding extra invisible stuff to make the equations work is justified

IANAP but here’s my understanding.

At the end of the month you spent $2000, you’re not sure how so you track down your expenses:

  - rent $500
  - groceries $120
  - gas $80
  - …
  - unknown: $123

That ‘unknown’ is dark matter. It’s a placeholder. It’s there and makes your total but you can’t explain it yet.