This has been answered many times. The policy is covered in Rule 240 of the Delta Contract of Carriage, section B.

"At Delta’s sole discretion and if acceptable to the passenger, Delta may arrange for the passenger to travel on another carrier or via ground
transportation."

Note the "at Delta's sole discretion" part. So, they may put you on another carrier, but there is no obligation in the CoC to do so. Not surprisingly, they will give preference to status holders. Also, the nature of delay (weather vs. mechanical, etc.) will generally have some bearing. With flights often running at close to 90% LF's these days, it's often the case that they simply can't accommodate everyone on other flights. Ultimately, they are going to strongly favor putting you on their own metal just as the other carriers do. I suggest you try to demand that WN put you on another carrier in IRROP's and see how that goes. When there are extenuating circumstances, such as a elderly grandparents, it's best to explain the situation calmly and rationally and acknowledge that while they are not obligated to put them on another carrier, you would appreciate their understanding.