I can think of only one answer: DRM.
Or rather, anywhere you have a system in which the consumer must be able to decrypt and consume the encrypted data in a controlled fashion, but at the same time must not be able to do so freely.
Consider, as an example, a 2D game with user-provided content, where users can create graphical assets for their own areas, but don't want other players to be able to steal those assets for their areas.
Now, this requirement is physically impossible for any large volume of user-created assets - the data must be decrypted to send it to the videocard and display it. But people dislike having their work ripped off. The obvious primary approach is to take a social approach to it: make it just plain uncool to rip off people's work, name and shame, assist 3rd-party toolmakers who play nice, censure those who don't, provide in-game admin policing of reported copyvios, assist in legal disputes... but that's all super-high-overhead, taking immense amounts of admin time, so there have to be technical methods to help.
And you can only get so far with automated dup-checking of uploads, using custom filetypes with custom editors which track attribution history, and so forth.
So the hurdle is to make it harder to steal a graphic by decoding it, than it is to steal it by other possible methods (screenshotting, etc).
All you're doing there is scrambling, you're not encrypting, because you can't legitimately call something encryption if you're handing the key to every possible recipient ever.
And the end result is that you end up with an arms race, where you permutate, tweak and improve your scrambling a little each release. You can't even make it the very best scrambling that you could, because then once they cracked that, you'd not have anything further to move to in the arms race.
Edit 1: So why not use an open algorithm? Well, with DRM, your only defense against cracking becomes security through obscurity. Using standard crypto is a significant disadvantage here, as it is explicitly designed to be as non-obscure as possible. It will be the first thing people try; there are plentiful libraries for them to use to make code to attack your data; and there is plentiful documentation and people with skill in using them to answer any questions the hackers might have.
Edit 2: The question description says: "Obviously this phrase has been hotly debated and surely is only acceptable if discovering the mechanics of a proprietary algorithm doesn't actually reduce it's security."
I do not believe that this argument holds water, in a logical sense, either for DRM or for real encryption.
If revealing an algorithm doesn't reduce its security, then there is no reason not to reveal it.
There is also every reason TO reveal it. Revealing has advantages, while concealing it has none. A concealed algorithm has no trust. If you reveal, you can also patent it, you are then protected from theft far better than just hoping that someone doesn't reverse compile it. You can also bask in the attention and adulation of the crowds for creating an impenetrable algorithm that was better than existing open solutions.
Concealment just suggests that you have something to hide: that you feel you need the security through obscurity. Only DRM needs that, and that's only because "DRM encryption" is an oxymoron.