As might any plaintiff. NYT might be the first of many others and the lawsuits may not be limited to copyright claims
Why has OpenAI collected and stored 20 million conversations (including "deleted chats")
What is the purpose of OpenAI storing millions of private conversations
By contrast the purpose of NYT's request is both clear and limited
The documents requested are not being made public by the plaintiffs. The documents will presumably be redacted to protect any confidential information before being produced to the plaintiffs, the documents can only be used by the plaintiffs for the purpose of the litigation against OpenAI and, unlike OpenAI who has collected and stored these conversations for as long as OpenAI desires, the plaintiffs are prohibited from retaining copies of the documents after the litigation is concluded
The privacy issue here has been created by OpenAI for their own commercial benefit
It is not even clear what this benefit, if any, will be as OpenAI continues to search for a "business model"
Wanton data collection