In my experience, Data Science isn't replacing statistics, it's replacing Business Intelligence. And a lot of that is driven by PR and marketing departments that saw that business intelligence was boring and trapped them in the IT department, so they needed new buzz words. You can see the relationship on Google Trends as well, and it's stronger than comparing it to 'statistician', which looks flat more than declining:

https://www.google.com/trends/explore#q=data%20science%2C%20...