Bing actually is
do a request in the background to log that info. It helps them collect that info and it makes them have a major power over their competitors.
Now, Bing and Microsoft actually went out and started fighting them, from a seriously underpowered position. And it's great they do, because otherwise Google would be the only search provider in the western world.
This is also the reason why Google is struggling in non-western world like China and Russia. They didn't get there by the time internet got wider usage, so they cannot get market share now.
Firefox with Google as default is a "join project" too. Mozilla depends on almost completely on revenue coming from Google. And unlike Slashdotters think, it's not a "here, take some money and make a great open source browser!". Firefox has (or, had) the market share required and Google wanted to be the default engine so they get users. And they pay a share of revenue generated by those Firefox. Just like Ubuntu, Fedora and other free Linux distros to generate their revenue. Not that's there's anything wrong with that, but usually Slashdotters try to somehow glorify Google. It's business as usual.
Personally, I use StartPage / IXQUICK
because it's European and values my privacy more.