It really depends on your needs I guess. Not to undermine them in any fashion but If you just need some generic features and get something out quick, a pre-built engine can take a lot of the head ache out of it. I'm thinking stuff like last years 'Skate Story', built by one guy over a few years and it looks great, all done in Unity. If they were building their own engine it probably would still be another few years back and probably for not much gain.

But then things like Fez as you mentioned, back in 2012 when it came out, it would have been a real struggle to put together with off the shelf engines. I could see it being much easier now but still a product of its time.

One studio I am endlessly impressed with is Enhance games. Tetris Effect (UE4),Rez Infinite (UE4), Humanity (Unity) and Lumines Arise (Unity). When you fire them up, you would be really hard pressed to know what engine they are running as they have made the end results so unique that the base engines traits are almost completely gone. That is a real talent.

But if you have some unique tech that just needs to see the light of day or a work p=flow that just doesn't fit what everyone else is providing, go with your own engine. There will never be a one size fits all.