http://imgur.com/7IqYMHD

(Notice also how the current search engine being used is represented with icon and name.)

Clicking "Change search settings" brings you to a dialog which clearly gives you the ability to set the default and remove unwanted search-engines:

http://imgur.com/qSM0BAd

Yes. It's one more click than it used to be. But now it's visually 100% clear what it does and how it does it.

The previous incarnation required one less click, but my guess is that most users didn't even know they had the option to change defaults or remove search-engines since it was not spelled out explicitly.

It may not address all your concerns, like suggestions on non-default engines, but I think overall it's not 100% a degradation either.