Isn't that a safety thing? To shutdown a natural gas plant you just close some valves feeding the facility, or at worse introduce something into the combustion path that halts combustion. Nuclear fission obviously can be moderated, but not in such a sharp and safe manner.
Thermal-spectrum (slow neutron) nuclear reactors are much easier to control than fast reactors because they have much slower reaction times. But this isn't particularly relevant because thermal-spectrum supercritical water reactors are possible; supercritical water reactor doesn't implies fast reactor. Let's put fast reactors aside.
In thermal-spectrum reactors, the moderator is not in itself a safety feature. The moderator is necessary to slow the neutrons down into the thermal-spectrum. Thermal-spectrum neutrons are far more likely to be absorbed by the fuel than fast neutrons, so if you lose the moderator the reaction stops (and decay heat continues...) Fast reactors don't use a moderator and don't need one because they use a higher grade of fuel which can sustain a chain reaction with fast neutrons, not needing thermal neutrons.
In some thermal-spectrum reactors (particularly BWRs and PWRs), the moderator plays double duty as a coolant. In these reactors the moderator is a safety feature insofar as it's the coolant, not because it's a moderator. In other kinds of thermal-spectrum reactors, the coolant and moderator may be different; for instance RBMKs use graphite as the moderator and water as the coolant. Modern CANDU reactors use heavy water as a moderator (which is less efficient as a moderator, but captures fewer neutrons and therefore allows for a lower grade of fuel), but this moderator is unpressurized in the calandria and remains cool; the water in the coolant loop is hot, pressurized, and doesn't provide sufficient moderation to keep the reaction going. If you drained the moderator but kept the coolant loop running, the reactor would stop. If you kept the moderator but drained the coolant loop, it would eventually melt down (probably after the water in the calandria boils off). The coolant is what removes heat from the reactor and the moderator is what slows the neutrons so they're more likely to cause fission.
tl;dr: The moderator increases reactivity. Coolant removes heat.
In principle you could make a thermal-spectrum supercritical water reactor using any of these, but the research is aimed towards making a supercritical reactor with the PWR or CANDU designs. The reason supercritical water reactors aren't used yet is because metallurgy isn't up to the task. Supercritical water is already used in traditional power plants, but those don't have to deal with neutron radiation which structurally degrades anything it runs into (some alloys/materials more than others.) Finding alloys which can hold up to both supercritical water and neutron radiation is the major hurdle to clear.
Ahh right... The neutron corrosion. Same problem with fussion reactors.
The problem is, there is no material that can survive this imo.
The only one we know that can, exists in neutron stars and its ultra dense.
Its unusable by us (different structural scale).
I think what I was trying to convey was you can always undergo the scram action on a nuclear reactor to halt it. The problem with this is in some cases, this mean restarting the reactor costs more than the value of the electricity it will generate before refueling.
Well, you could scram a supercritical water reactor too. If there's an emergency that warrants scramming the reactor, the time it will need to restart should be low on your list of priorities.
As for refueling, in some designs like CANDU refueling can be done 'online', refueling one tube while the others are running.
