As I said I was following up:

I did get an explanation, but unfortunately I'm legally not allowed to share it with you. I can tell you this much: Opera didn't swap Bing with DuckDuckGo because they felt like it, but they did so for a reason. IMO Opera's non-communication policy often offends people and isn't the best idea after all, but as I'm not working for them, I can't change that.
I'm going with solution number 2 (out of my mentioned comment). I was reassured by Opera's devs that they really want this to happen themselves. They just didn't come up with a solution yet that prevents third-party programs from fiddling with your search engines.

I get that this maybe isn't exactly what you guys wanted to hear, but I also think that it's good news that there's hope for custom default search engines to happen eventually. And maybe you can even help making this happen faster:
Does anyone in here have an idea how to solve mentioned issue?

This is not possible. Any program or file on a computer can be read and modified by other programs. Even if you encrypt it you'll be able to read it and change it. Grab a hex editor and start hacking. If they truly intend to solve this in that way they will never have a solution. We already have solutions to crack their default search engines. How is this any different? The only solution that 'might' work is to route all searches through Opera servers and select the proper search engine to use based on data maintained server side. This is less than optimal (if Opera servers die you can't search, you need an account or this doesn't work etc) and could be worked around still.

Sounds like I need a new browser. Clearly Opera's priorities need to be reevaluated.

Definitely not the same people, just a lot of people that are coming from the shadows. Poor product management tends to do this. I actually had an account years ago, it got deleted for reasons I do not recall.

To address the personal attack by blackbird (I hope you understand the irony of your immaturity comment!): This is due to the fact that 1) this is a feature that already existed. 2) this fix is trivial. 3) Opera should know better than this. The omnibar is a huge feature to have destroyed overnight and should be top of their PO's list. If it is not than our needs and intentions for browsers are not the same (not even close) and they are no longer worth the trouble.

It is the metaphorical removal of the start button.

the Bing search engine inclusion deal Opera Software had with Microsoft just expired and MS decided to not renew or pay the value Opera was asking for it. Opera then replaced it with DuckDuckGo either because they made a deal with them or by "philanthropy".

I doubt this considering that it is still included as the search for "define *".

I will be leaving as well (User since Opera 10) if Bing is not restored. Every change since 12 has can hardly be called a correct one and the degradation of the final feature I came to Opera for is unacceptable. You have taken my speed dial, my search customization, my mail, my irc and series of other features.

You have until Friday night to remedy this (patch downloaded to my PC). That should be ample time to both develop and test the return of a search engine.

I will no longer recommend Opera as a result of this, no matter the resolution of this. Such poor product management deserves anger.