As long as Bing doesn't get direct access to the metadata of the device making the query why does it matter? I assume they're not using the Bing API straight from the client browser, are they? They're basically proxy-ing Bing's results and add their own features on top of that. At least that's how I understand it.
Privacy is one but not the only problem with centralised web search.
The other big problem is manipulation of search results.
Of course it already happens for ads and filesharing and that is bad.
But worst is when they do it for political reasons. Bing cannot tell who you are, but they can still promote their own agenda by tweaking the ranking of search results. Blog against MS? Send it to the 10th page or hide it entirely. Of course I use here a very innocuous example. You can imagine the power of tweaking search results. You can change the perception of reality, essentially.
Well, you're still sending information to Bing. For example, let's say you want to know if someone patented idea X. You can search for X on Qwant, but since they send the information to Bing, now Microsoft knows about X and they can scoop you. Just one example.
Isn't that what DDG is using, as well?
Bing happens to have quite a good privacy policy, afaik.