I perfectly understand it when a bunch of scripters and artists meet to create a carbon copy of Gears of War or something originating from the same pipeline established for them.
But if you are someone who wants to be in exact control of mechanical interactivity (gameplay, physics, collision etc.) and code system architecture it is hard to see a benefit to it. I would feel more safe to create my own engine than hunting down the bugs in a foreign one.
As someone who has been writing their own engine for a while now, I strongly disagree with this statement. Writing your own engine is a big investment of time and effort that should not be taken lightly. As well, there's a huge amount of experience and knowledge that you need to have to make an engine with an architecture that will even remotely keep up with a modern professional game engine.
Modern game engines have tons of tools to give a custom look and feel to a game. Keep in mind that Mirror's Edge is an UE3 game. Even more, an existing engine has tons of tools to make those things that give your game your own feel work across multiple platforms. Shader code isn't easy to port and keep efficient across all frameworks, drivers and platforms.
Even more, there's a huge existing toolset and support community you're throwing out of the window when not going with an established engine. Having to write your own editor adds another extra few months to the development timeline, and as a result it will probably still not be as good as what UE4, Unity or CryEngine have to offer. As well, Unity has a huge asset store available for use with tons of great easy to plug in components for your game. (though I personally really think they should at some point support NuGet as well)
Dismissing using an existing engine as just being for making carbon copies of existing games trivializes a lot of people's hard work.