[please]

so having just one input for url and search was not such a good idea, for privacy.

[paulgb]

To me, the advantages outweigh the costs, though. If I want to search for something without Google knowing about it, I can jump to incognito mode.

[stanleydrew]

This occurs even in incognito mode though.

[babar]

Incorrect. Incognito mode does not use the search provider's autocomplete results.

[stanleydrew]

Interesting. I hadn't noticed that, but you are right. I only get suggestions for searches I've made during my incognito session (so stored locally in the browser's memory) or for pages in my history for that session.

[axod]

... for the small niche set of users who care about such privacy over usability.