https://blog.mozilla.org/ux/2014/11/find-it-faster/
What are you talking about?
* Extra clicks to use non-default engine, especially for multiple searches in a row.
* Options to add/remove engines or change the default are very well hidden.
* No way to get suggestions from the non-default (or just stop asking the default for suggestions at all, if your default is Google/Yahoo/etc.). Prime example is Wikipedia autocompleting from page names - now not possible unless it's your default.
* Always by default assumes you want the default search engine when you might want to switch back and forth with your active one.
* No indication of what the default search engine even is.
* Looks stupidly messy with 12+ search engines (seriously, do you only use google or something? Once you have Google, DuckDuckGo, Wikipedia, Google Images, various wikis and news sites all added, it's a total mess with the new clusterfuck of a UI).
* Searching through a list of favicons sucks compared to having a dropdown with favicon and name.
* Broken keyboard shortcuts.
(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:
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.
Mozilla recently reworked their search bar to make it much harder to change the default (coincidentally, at the same time as they changed it to yahoo... imagine that ;) ).
You can get the old one back in about:config:
browser.search.showOneOffButtons = false
Completely agreed on google and matching - it's got too 'smart' for its own good, and when I'm searching for specific words, it often 'helpfully' includes results for the complete opposite too, or for reversed word order that completely changes the meaning (e.g. foo guide for bar users == bar guide for foo users according to google). If I'm looking for anything at all specific or complex, I use DuckDuckGo or even Yahoo. I try to use DuckDuckGo day to day when I can too, of course, for privacy reasons.
The rot started when google stopped supporting boolean operators, +, and "".