I thought I'd provide an anecdotal supporting example to show that there are valid exceptional use-cases that don't practically fit into a pre-existing 3D engine -- specifically, a 3D visualization of a space-scale procedurally generated universe with trillions of stars and planets.
Several times I tried expanding an existing modular 3D engine (OGRE) towards my goal of displaying a huge virtual universe of planets and stars. While I got it rendering 3D planets after some work (where I basically had to implement manual rendering code anyway, since the engine didn't support the odd use-case of spherical terrain), contorting it to support massive coordinate spaces, huge view ranges, dynamic loading/unloading etc. was just far too messy to even hope to attempt in that engine.
After several attempts to cleanly implement a space-scale engine as an extension of an existing engine, I started over from scratch using pure OpenGL (WebGL). And this time, I managed to keep the code reasonably tidy while supporting trillions of stars, planets etc. as I had originally planned [1].
Would I have been able to do the same thing in OGRE if I kept trying? Probably... but likely with far more ugly code, terrible hacks, bloated engine, and slower loading times.
To be fair, I'm not advocating always "rolling your own" 3D engine. It's usually a huge task, and using a pre-existing engine will in almost every case be the smarter choice. But with some people trying to argue "you can make it fit in [Unity/OGRE/etc]", I thought I'd provide at least one anecdotal counter-example.
1. Kosmos: A virtual 3D universe in your web browser (https://github.com/judnich/Kosmos)