1) If it explodes on takeoff you're fucked
2) Naval reactors (and all reactors) require massive heatsinks to dissipate entropy. There's no ocean in space.
Space-based nuclear energy is all based around RTGs, reactors have no place in space
RTGs, on the other hand, are radioactive from the get-go, but are usually quite small.
The USA did run a reactor in space (SNAP-10A) and the Soviets did a few dozen.
Also the problem isn't running the reactor on the launch pad, the problem is if the launch vessel explodes and the fuel load gets spread out over your launch area. The enriched uranium used in naval-style propulsion is absolutely not "safe to hold in your hand" and the weight requirements for using natural uranium, which is safe, would be prohibitive for use in space.
[1] https://en.wikipedia.org/wiki/SNAP-10A
Highly enriched uranium is still barely radioactive, very similar to natural uranium. The half-life of U-235 is 703 million years. As half-life approaches infinity, atoms approach stability. The dose rate of holding navy nuclear fuel is modest compared to the hazards of fission products.
The on-contact for a HEU billet is over 10mrem/hour. You and I have very different ideas about nuclear safety apparently and I presume you haven't worked professionally in the field with that attitude.
According to that Wikipedia article, SNAP 10A was centered on a device that created and maintained a controlled, sustained nuclear fission reaction. I would call that a "nuclear reactor" even if no attempt were made to harvest the power. I think that the rest of the world is probably with me on this. The Chicago Pile 1 is widely regarded as the first nuclear reactor, and nobody particularly cares how it generated electricity. What they care about is that it demonstrated a controlled, sustained nuclear fission reaction.
You are getting the absolute basics wrong, so you have no standing to question the OP's atittude.
Nuclear reactor runs a nuclear chain reaction, hence the name, RTG does not. There is no scope for debate here. The difference is night and day and is obvious if you look at fuel, power to weight ratio, or do physics 101.
RTGs run on decay heat and use plutonium 238, they cant be turned off, their power slowly drops off over decades. Reactors use U235, have active control and starting/stop procedure and 10-100x higher power to weight
That said, it seems like, all by itself, conversion efficiency is a tricky measure of the usefulness of a design for spaceflight purposes. Wouldn't it be more useful to consider the total cost to deliver a given energy production capacity to space? In that case, rocket fuel itself, and the tyranny of the rocket equation, becomes a major consideration. If an efficiency gain comes at the cost of increasing the weight of the energy generation system in some way, then perhaps it doesn't end up being a net win over the less efficient design.
By comparison the voyager probe RTG used ~1/10th the fuel for a little over 1/10th the power. https://en.wikipedia.org/wiki/MHW-RTG So the only advantage was cheaper fuel.
The same reactor couod be hooked up to a 20% efficient stirling engine to keep it low maintenance, to a >50% efficient convined cycle or have 0% electricity output and be used for heat or water desalination.
By comparison SL-1 a 400kw thermal design so 4x power used a 12,000 kg pressure vessel including shielding. https://en.wikipedia.org/wiki/SL-1
It is true that RTGs are the only type of nuclear power used in space now, but that is more to do with type of craft we send to space rather than practical limitation of nuclear power in space.
A large spacecraft will have enough surface area mount enough radiative heatsinks to dissipate the heat from a nuclear reactor. Designs exist that have the math worked out for this since the 50s.