Normal reactors do shut down when the power fails. the control rods lose power and fall in. The hard part is cooling the reactor afterwards due to nuclear decay heat. Normal reactors use double-redundant super-reliable diesel generators to do this. This works fine until you out your diesel in the basement in a tsumani zone. Ebr-2 can shut down without CR insertion (crazy robust, CRs always go in) and then can cool itself without external power.
We'll have to go deeper in to the history and physics. The first reactor was passively cooled by air. It was very low power and didn't split very many atoms, so the nuclear decay heat was low after shutdown. Many reactors have been made that cool with natural circulation of air or water but they're all low power. Quickly, the Manhattan Project came along and the military wanted enough plutonium to make an atomic bomb to fight the Nazis. They built a reactor that could do this out at Hanford (the B reactor). They realized that to make enough plutonium, they'd have to increase the rates of the reactions that produce it. This required splitting more atoms, which released more heat, which required more cooling. They quickly went past the regime where it was possible to use natural circulation with the known coolants at the time (air, water) so they used forced flow, eventually passing the heat into the Columbia River.
Fast forward to the 1950s. Admiral Rickover wants nuclear powered submarines to effectively fight the Russians in the Cold War. Submarines are small but want high power, on the order of a few hundred megawatts. This puts them beyond natural circ decay heat removal regime for air and water. So he builds them, and installs appropriate redundant backup systems.
Now Eisenhower has given the Atoms for Peace speech and the commercial industry is starting. They can build a compact high power reactor or large low power reactor (recall it's a heat removal issue). They choose compact, high-power one modeled after the Naval reactors. They were running great and had a whole supply chain. The low-power ones would be orders of magnitude more expensive per kWh.
Meanwhile, starting in the late 1940s and continuing for a few decades, exotic-coolant reactors were developed, with things like Mercury, liquid sodium metal, molten salt, organics, aqueous homogeneous slurry, etc. These reactors can do high power compact cores with passive natural circ. Many were built and operated. But they remained exotic and underdeveloped. The Navy and commercial nukes had built up an infrastructure and experience base. Exotic reactors were more expensive and the LWRs were fine instead of passively-cooled ones.
Today, dozens of startup companies have dug up the paperwork on these exotic reactors and are rushing to try to develop them and associated supply chains to build them cheaply.
So that's how we ended up with the reactors we have.
