Why are so many languages written using the Dwarvish script?

If you look at the list of Standard Languages, you’ll see that most of them use Dwarvish as their script:

  • Common: Common
  • Dwarvish: Dwarvish
  • Elvish: Elvish
  • Giant: Dwarvish
  • Gnomish: Dwarvish
  • Goblin: Dwarvish
  • Halfling: Common
  • Orc: Dwarvish

(While that’s 5e, I found a similar chart for 3e.)

The Forgotten Realms Wiki calls this script Dethek and explains some of its history, but I can’t see how the explanation there relates to the Standard Languages at all. I also know next to nothing about DnD in-universe history.

Is there an in-universe explanation for as to why these languages all use the same script?

I don’t particularly care where the explanation comes from as long as it is from some DnD canon where the premise is true. I don’t expect too many settings to have an explanation at all, which should keep this from being too broad.