What is t here?

I assume they meant T^4 radiation (Stefan-Boltzmann law): https://en.m.wikipedia.org/wiki/Stefan–Boltzmann_law

Nuclear reactors run at cool temperatures compared to say gas turbines. And they are powerful. So the surface area for radiative cooling is proportional to the power divided by temperature to the fourth power. So the cooling would need to be very big.

Right, but there is no shortage of metals and ceramics that can maintain cohesion (and strength!) at high temperature -- I'm thinking about those videos the machinists post of tools slicing through metal at an obscene rate with incandescent tooling. You don't even need ceramics to do that, there are steel alloys that stay hard and strong enough to slice through (soft) steel while incandescent, although for wear optimizaton they typically only actually do it with ceramics. In any case, it seems like someone should be able to figure out a "retract rods, let them glow" mode that dumps the energy into the sky like a lightbulb.

I'm sure there's a reason why it hasn't been done. Maybe you really do need high enough temperatures that you can't engineer compatible cladding, or it's hard to make IR windows low-loss enough to pass the energy, or something. Still... fourth power! The temperature you need the "lightbulb mechanism" to withstand is the fourth root of power/area! That's a powerful wind at one's back! It's easy to think of reasons why it might be impossible but if it's "just" a hard engineering problem then that's where things get interesting.

My non-expert guess is that given the large amount of power you have in a small area in a nuclear reactor, it would be hard to reach equilibrium while keeping the fuel solid.

If the fuel is in a liquid state (as in a molten salt reactor), then you could more easily since you could have it pour into a wide container, increasing surface area. (Basically the freeze plug approach).

It would be more possible for a high temperature reactor that can stand the high heat. A regular low temperature reactor would require a huge radiator for the same power.