Nuclear thermal rockets aren't that great either, the temperature and thus the specific impulse is not very high, and they have high dry mass and would be really expensive to develop and hard to make reliable.
In space you have 1.3 kW per square meter sun power constantly without the atmosphere or clouds in the way, and solar cells improve constantly.
Regarding the many comments in this discussion about accidents during initial launch: if nuclear thermal rockets are fueled with uranium 235, and don't reach criticality until after the risky chemical-booster ascent out of atmosphere, they should be quite safe. Uranium 235 has a 700 million year half life, hence very low radioactivity. The fission products from a live reactor of course include very-short-lived, very-high-radioactivity nuclides. But you can have nuclear power in space with extremely low risks to the terrestrial environment if you use it only for missions that leave Earth orbit, and turn on the reactor only after the risky initial ascent on chemical boosters.
That said, I agree that it would be expensive to develop nuclear thermal rockets. It's very expensive to test them on Earth, since the exhaust carries away some small amount of fission products and people don't just tolerate such radioactive pollution like back in the 1960s. You'd need some very expensive/elaborate test facility that can capture the hot, radioactive exhaust, or you'd need to do all the actual testing in space (also expensive/elaborate).
A chemical hydrogen-oxygen rocket might have exhaust velocity of 4.5 km/s so mass ratio is exp(6/4.5) = 3.8.
A nuclear rocket with exhaust velocity 9 km/s gets a mass ratio 1.9.
Most likely the nuclear rocket uses hydrogen only, meaning the tank is likely bigger than the chemical rocket's! The thrust to weight ratio of a normalish solid nuclear engine is about ten times worse than a chemical one.
You do save on the oxygen mass, but that's it. It's probably bigger, heavier, more complex and definitely more expensive and dangerous than an ordinary chemical rocket.
For higher velocities, it starts making more sense...
On Mars, solar power per square meter is a bit over 550W.
It's an unusual methodology to begin by looking up the power output of the sun, which is worked out using the reverse of your calculation. Might you have erroneously divided out the entire of Earth's surface area (which is 4 times the area of a circle the size of the Earth)?
We use solar cells at Jupiter distances nowadays (various reasons for that though).
You don't have gravity so you don't have convection or separation of gas and liquid. Hard to test such systems on Earth.
You can't make repairs easily.
Solar cells start to look really good really fast.
Maybe on Mars surface they could make some sense, or on the Moon where the night lasts for two weeks. Though on the Moon one would preferably settle near the poles without such problems.
But even on the surface, just regular batteries look really good on the simplicity front, and fuel cells beyond that.
This is what I thought. To my (admittedly fairly uninformed) knowledge, nuclear power is really nuclear steam engines, at least the ones I know of. As awesome as a space steam engine sounds, it doesn't seem too feasible for the reasons you presented.
https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_ge...
Though nowadays you could maybe improve them with advanced quantum technology, like long wavelength solar cells. The cell itself still has to be cooler than the source, so you still need radiators... https://en.wikipedia.org/wiki/Thermophotovoltaic
A steam turbine nuclear reactor is a Rankine cycle heat engine, their efficiency is above 40%.
The reason RTG are used is simplicity and no moving parts, but efficiency greatly suffers. If we could figure out more efficient thermocouple all sorts of opportunities open up, haven't seen much work in this area.
That nuclear powered space travel is more economical and efficient at large scales isn't disputed by experts. The barriers reaching that scale are funding and political, not the engineering ones you've highlighted.
If you can invent any kind of technology at will, sure, it can be great. Then let's have light and reliable space nuclear power plants. At the moment we are very far from that.
It might have looked like a good choice forty years ago, but solar cells have improved a lot, as well as batteries.
We do have some newish things on the nuclear side that could help, like gas cooled reactors or supercritical power cycles. You need to get the temperature up (to make the radiators small) and the power density too.
We are much closer to the tech for efficient nuclear rockets than we are to the tech for an (even partially) self-sustaining colony on Mars.
People have done the calculation and nuclear would be way, way better then solar for a mars colony.
(What's all this about cloud cover?)