As a general rule, we can say that there is no reason to use a difficult interface if you can use a simple one, although there are situations where it is acceptable and even recommended, and if you have to do it, it's better that it is easy to learn but with all the required element than easy to use and lacking necessary elements.
For instance, Microsoft Office, had the same interface for years, which made that design a solid standard, but we all know how for the 2007 suite, they decided to change it to a more modern and flexible one. Most people hated it, and due to the fact that it was new; plus people didn't liked it (the reasons are not important), it became very difficult to use. We can say that it was difficult by itself, with out the emotions involved, but that doesn't change the fact that it was difficult. Still, there was a reason, they wanted to add more features, and make all, or almost all of the existent features reachable with less clicks, which sounds very good, but the change made it difficult and people had to adapt to it. Most frequent users adapted quickly to it and learned the interface, so we can say that they did what you ask, they produced an easy to learn UI that was not as easy to use.
On this article from the MSDN blog titled Ye Olde Museum Of Office Past (Why the UI, Part 2), we can see some of the old interfaces, which are very similar to the next image. All those where easy to use because they where more or less the same, but though the years more and more features where kept in a difficult to learn interface, hidden on many levels of submenus.
And for those few which are not familiar with the more recent interface, this is an example, which look clean and easy to use, but it's not that easy or intuitive, but once you learn the grouping mechanic, it's relatively easy.
On the article Making User Interface Elements Difficult to Use By Intent, Jacob Gube gives good reasons and examples for why and when difficult interfaces make sense, this excerpt is a good example of the article:
However, a big part of designing user interfaces that are easy to use also involves figuring out what things should be a bit more difficult to use. It’s a counter-intuitive notion that’s central to effective user interface design.
Or this other quote, which on it self includes a quote from Jeff Atwood
So, if Fitts’ Law states that interface elements that are essential to the user should be bigger and closer to them — or in the context of a computer screen, easier to find and see — Atwood looks at the problem in reverse and asks, "What should we do with UI elements we don’t want users to click on?"
The answer is simple. By logic, we make those UI elements more difficult to use, locate, and find by making them smaller and more distant to the user.
Although, for me, the most important reason is at the beginning of the article:
When there’s an overall improvement to the UI as a whole
Benny Skogberg already covered the situation where a difficult interface has a reason based on the specific use of an specialized group of users, which should also have training. I'll add that some times, even if there is no training, certain tasks require complex interfaces, for instance 3D software like 3D Studio Max or blender have very busy interfaces, but they require almost all of that, and if you remove it, it will feel incomplete, so they are difficult to use and difficult to learn; in deed they are considered so complex, that they rely heavily on using keyboard shortcuts, that way, the interface and the space to work can be optimized.
