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The F-22 was probably used in the most popular case as a show of force.
Fighter jets don't just sit in hangars all day. They're no good without trained pilots.
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.
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.