Hi guys,
There isn't an ability to wholly turn off people detection at a tenant level but it is a great idea. There isn't a Uservoice for Stream like Office 365 or Teams. However, I have raised this for you at the Microsoft Stream Ideas which you can now vote on -
https://techcommunity.microsoft.com/t5/Microsoft-Stream-Ideas/Ability-to-turn-on-off-people-detectio...According to the following article owners of the video should be able to hide people in the timeline, but this is very much a workaround to what you actually need.
https://docs.microsoft.com/en-us/stream/portal-find-facesHope I answered your question. If I have please like and set as the solution. If there is anything else you need please let me know! Hope to answer more of your questions soon!
Best, Chris