My 3yo wanted purple mash potatoes, it didn’t really work because I used yellow potatoes. Then my 3yo decided she didn’t want potatoes so my wife and I were stuck eating prison gruel.
The potatoes never stay as purple as you'd like.
We have these in NZ: https://www.tepapa.govt.nz/discover-collections/read-watch-play/maori/maori-potatoes (last image on the page).
They start out the bright royal purple in the image, but by the end of boiling they turn a blueish-grey colour, and the water will be a delightful maroon-crimson shade.
If you want it to look like you've blended up Barney the Dinosaur, you're going to be colouring them.