The way I've heard this explained, fuel is 3% of the mass of a modern car, 45% of the mass of a passenger jet, and 90% of the mass of a rocket. That means the structural engineering margins of safety for a rocket are much smaller, as there's very little mass fraction available to build redundancy into. There just isn't a lot of 'rocket' in a rocket. That, not complexity, is the root cause of why rockets aren't so reliable.
There's an even more basic physical reason why 'rockets are hard'. It's easy to explain in energy units of kT, the approximate energy of a gas molecule at room temperature. A carbon-carbon bond has an energy of 140 kT, while the gravitational potential energy of a carbon atom on Earth is 300 kT. If the Earth's gravitational potential were much closer to kT, room-temperature gas molecules would be able to diffuse out, we would have lost our atmosphere to space, and humans wouldn't exist. But that means that for a chemical system to escape Earth's gravity, needs a clever arrangement whereby most of the energy contained in its chemical bonds goes to a small fraction of its molecules. In a way, it's surprising not that chemical rockets are hard, but that we're lucky enough to be able to use them at all.