Why do missiles have fins, while modern space rockets don’t?
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Missiles operate either partially or entirely in atmosphere (depends on the missile) and in the atmosphere fins are very cheap and effective ways to maintain stabilization. You don’t need any fancy technology to dramatically improve the missiles, just slap on some fins and boom, a much more accurate missile.
Space craft, however, operate almost entirely out of atmosphere in a vacuum. Since vacuums have no air in them fins are literally useless. So if you add fins to a spacecraft you are just wasting money (even more so than you might think, because it’s not the fins themselves that would cost much, it’s the extra weight they would add that would mean having to use more fuel which is expensive.)
That said, there have been spacecraft that have had fins, most notably the space shuttle, but the only time that ever happens is if the spacecraft is planned to spend a decent amount of time in the atmosphere, like the space shuttle did when it would land for reuse.
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