Depends on the idea. I started with mods and early game makers in the 1990s then prototyping in C++ with basic libraries like SDL. To make Pong it didn't matter much. To make an epic 3D FPS the engine was a do or die decision.
It was do or die, but you could pick an engine right?
There are engines that will allow you to do a 3d FPS and make it look very good without ever having to worry about any low level barycentric coordinate issues.
It is good to have options. It's just that using an off-the-shelf engine means fitting your idea into that square hole. Or else you'll spend time fighting it. And for games imagined with a distinct visual style that may be a lot more or less work depending on which one you choose.
