That’s not true for any post 1995 desktop CPU.
They just adhere to that model and pretend that that’s all they’re doing but in reality there’s layers of supercomputers inside the CPU: micro-op cache, branch predictor, reorder buffer, rename buffer.
They extract hidden parallelism out of the code, run it in blazing fast multiple instructions per clock cycle (!), and pretend that nothing out of the order happened.
CPUs are extremely complex and extremely smart. They can have errors in their implementation where the unseen branches that it executed can be accessed by some processes, etc. But there’s nothing dumb about CPUs. They are made of a million man-hours of engineering.
What's the difference between a logic gate and when my index and thumb have a static charge jump between them? About a couple trillion dollars of research.
That seems to me a highly reductive point of view. The whole is always more than the sum of its parts.
This is the one I played some time ago: https://nandgame.com/
The GameBoy CPU is simple and easy to understand, sure, but modern ones are built upon the same basic principles, it's just that they run at much higher clock speeds and add lots and lots of parts (caches, pipelining, speculative execution, register renaming, multiple ALUs, SIMD ...) to execute as many instructions per clock cycle as possible. Also virtual memory support — MMU, TLB, all that stuff.
For the other side, if you want to build a CPU out of logic gates, there was a web-based game where you did exactly that. I don't remember the URL, sorry.