The power dampening chip was implanted to save Nora's life
Nora's feeling the hurt for discovering that she had Super-Speed like her father, and her mother took that away from her, but it's likely that there were some serious side effects which Nora was too young to remember.Taking inspiration from the comics, there are two options:
- Nora's speed was killing her (like Wally West's in the early '80s)
- Nora couldn't slow herself down (like early Bart Allen)
It doesn't even need to go that far: an infant or toddler with super speed would obviously be a danger to their own safety. And if Iris is raising Nora alone, she can't count on Barry to keep tabs on their superhuman daughter.
This could also work in another way. If Legends of Tomorrow is any indication, society isn't too tolerant of metahumans in the future. If Nora had Super-Speed, she'd likely be targeted by A.R.G.U.S. and thus her losing her powers would prevent her from being a target.
