I remember reading somrthing...
... once. Something Oppenheimer (or it might have been someone else) said after the atom bomb was tested, or after it was publicly used. Whoever it was, they said it wasn't the 'spies', the Fuchs et al, that gave the atom bomb to other nations. I mean, yes, those folk maybe speeded things up a little - but they didn't 'give the secret away'.
The Americans did.
Because, whoever it was said, it wasn't 'how' to build an atom bomb that was hard - any halfway decent physicist could do that. But they could only do it <u>once they knew it could be done</u>. Or rather, it was much easier to start, to get funding, to put a project together, when the people paying you knew you weren;t just going blue-sky - you were just going to repeat something pretty obviously able to succeed.
Backdoor encryption? It could be just like that.
If you're a nation state, or a criminal, or script kiddie in your mom's basement, yes. You can go looking for possible security holes in all kinds of things. But if you're a _real_ black hat? Well, if you know Guv'mint X insists on backdoors, and Guv'mint X allows Product Y to be used? Well, you know the only reason you don;t know the backdoor into Product Y is because you haven't found it yet. Because whether they admit it or not, whether they publish it or not, just by allowing Product Y to be used, Guv'mint X is telling you the door is there to be found.
And, just like the atomic bomb, knowing the door is there will likely make it a damn sight easier to get the resources, or project approval, or just sheer bloody mindedness that will _let_ you find it.
Because you know it's there.
And it won't just be one - one hypothetical black hat, I mean. When folk _knew_ there was gold in the Klondike, they didn't say 'hey, let's not go there! Let's go look at some other damn river, it'll be quieter!'
They Rushed, and even if not everybody found gold, a lot did. But the Klondike? It was never the same again, and after a while - it was dead.
So, yeah. Guv'mint approved apps. With Top Secret Guv'mint backdoors. Because sometimes, all you need to know is where the gold exists - finding it's the easy part.