[seanmcdirmid]

Rocket engines are simpler than jet turbines, actually. It take a lot of material engineering to get something with both performance and economy. As for the rest, it’s just avionics that china hasn’t developed yet, and that really “just” software.

[npnpnp]

By that logic, scramjets are the simplest of all!

But really, there’s an order of magnitude more engineering that goes into so many facets of rockets and rocket engines. On paper they’re similar, but the stresses and constraints are much, much higher.

[seanmcdirmid]

Rocket engines point up and ignite the fuel. They don’t need air intakes, nor can they benefit from them. They don’t need to be reused (SpaceX’s strategy isn’t common). Rocket engines came a few decades before jet turbines for good reason. Heck, there is a good argument they were invented during the Tang or Song Dynasty in some kind of crude but representive form.

[npnpnp]

It depends. SRBs are pretty simple (yet still incredibly hard to make remotely safe).

Orbital rocket engines are not “point up and ignite fuel.” You’re right, they don’t need air intakes - they need cryogenic liquid oxygen and all the support equipment involved in using it! Jet engines have it easy being able to harvest the oxidizer as they fly.

There are many, many, points of failure in modern rockets . You could argue that jet engines were the precursor to modern turbo pump design.

edit It’s also worth noting that the turbopump environment is dramatically more hostile in rockets. LOX is really nasty stuff at those temperatures and pressures.