I think it's a good idea not to write an engine.
But I also think that for most small games (1-2 developers) it can also a be a good idea not to use an off the shelf engine either.
Write the absolutely minimum that you can get away with to achieve the gameplay and look you want to achieve. Hard code everything for your specific game.
It's true that if you want to write an engine you can distract yourself from focusing on gameplay. But I think you can actually fall into the same trap using an off the shelf engine too. You end up spending a pile of time learning and working with the advanced tools and not focusing on gameplay either!
The basic rendering APIs are actually not that hard to use if you forget about generalising everything for some future that never arrives, and there is a hell of a lot to be said for working on a code base that one person entirely understands. The development speed benefits of this should not be underestimated.