A rare outage should cause an executive to think "let's make our own search engine index"? If for every partner outage i would go "let's do it ourselves' i would be long out of business
It should remind them their entire livelihood is dependent on one single company. They arent partners at all. Its more like one is sustenance/oxygen for the other
But are they? Not asking for the contract side here but for the technical aspect.
If DDG relies mostly on Bing and it fails forever in the future, they can "simply" make a contract with google and continue whatever they were doing.
Same for OpenAI. Its not that Bing is the only search engine index on the web is it ?
So yes, it would mean they have to spend a lot of manpower in a short time.
On the other hand, how likely is it that Bing just goes offline?
Do you always have a second datacenter in case your provider fails? Not everyone does it and as long as you have a way of putting things back up in reasonable time you are good to go.