I mean sure, they don't have to but it's still a crappy thing to do. Imagine if you couldn't open your docx file in libreoffice or google docs because Microsoft only wants you to use their own interpreter i.e. Office. It's not like DTS or Auro are stealing Dolby's tech. Rather, they are taking the existing audio codec and running it their own way. I am pretty sure you can overlay Dolby on DTS too. This just makes the battle for the dominant audio format a lot more awkward.
And Dolby has put this under the false pretense that they want to curate and enhance the customer's experience. If that were true, why would they still be allowing Yamaha, Denon or any other receiver manufacturer to overlay their DSPs over their signal? The first party processing by these companies is known to be far worse than that of DTS, Auro, etc.