A radiothermal generator uses the heat produced by radioactive decay of the radioisotopes contained to generate electricity. The main difference with nuclear reactors is that there is no "reaction", chain reaction or otherwise, just the natural decay of the isotopes.
Currently RTGs are used as power plants in situations where a power plant that works for several years without maintenance is needed. This is because an RTG doesn't actually need any moving parts to work. Such RTGs use thermoelectric systems and highly radioactive isotopes selected based on the desired lifespan.
But there is nothing stopping you from using less radioactive isotopes for longer lifespan or using more normal solutions for turning the heat into electricity. Using such RTGs instead of nuclear reactors would have some benefits.
Can use any radioactive material. Uranium, thorium, radon, nuclear waste... Since the RTG does not need to support a chain reaction it does not care what elements or isotopes you throw in. This should make fuel much cheaper to get.
Much simpler fuel refining. Since the RTG does not care about the specific isotopes and can't be "poisoned" by inactive material, chemical refining methods are sufficient. No centrifuges or other methods capable of creating weapons grade uranium are needed. Refining fuel creates no risk of enabling nuclear weapons development. Much lower level of technology and investment is needed.
Less waste. Much less waste. RTG works until the fuel is no longer radioactive. Normal reactors only use a portion of the fuel since using the rest would requiring refining the used rods to make new fuel, which would enable refining the fuel for weapons grade material. So much of the fuel is simply wasted.
Safer waste. The high neutron flux of a reactor creates new radioactive elements such as plutonium. The RTG generates less flux and generates less such material. And any such material would be much harder to separate even if somebody opened the generator while it is operating. So unlike a reactor the RTG does not help in generating material for nuclear weapons.
Safer. No reaction means the reaction can't get out of control no matter how many safety systems you disable. You still need a containment vessel and it still can rupture and release steam containing radioactive material, but since the RTG does not need or generate highly radioactive isotopes and a runaway reaction can't melt the fuel the level of radiation would be much lower than with a reactor. Which would help a lot with fixing the damage.
So if it is so safe and solves all nuclear proliferation issues, why aren't any being used? Economics. Such RTGs would be much larger than a reactor generating the same wattage. The RTG could operate almost indefinitely with little maintenance without ever needing refueling. But reactor fuel and maintenance are not expensive enough to make up the higher initial cost with any realistic interest rate. Although the fact that RTG would be much simpler and cheaper per volume would help.
So with that intro, here is the actual question. Under what circumstances, if any, could using such large RTG systems for base power become economical? Science based, but not real world. Alternate reality or history is okay if it makes sense and obeys the same science.
First question, btw. And something I have been thinking for a while.
From the first answers it seems that I did not properly explain how different these base power RTGs would be, would have to be, from the RTGs currently in use. I'll note some specific issues that were relevant to those answers. (And really necessary to understand the question and why I am unable to even suggest plausible economics.)
Current RTGs have relatively short lifespans and use "artificial" isotopes with relatively low half-lifes. The RTGs I am suggesting use natural radioisotopes of uranium or thorium. These materials have half-lifes of more than a billion years! (That is why they are still common.) Obviously the power density sucks big time. On the positive side it will take millions of years before the power runs out. On the negative side the installation would need to be huge beyond belief to generate useful amounts of power.
So these are not small (relatively) devices spread around that can be lost or abandoned. these are a small number of installations you can see clearly marked on the world map. Or with your own eyes from the Moon. This is because the only way to even approach usability would be to take advantage of cube-square law of the radiothermal energy going up with the volume (mass really) but of the mass (and thus cost) of the containment with the surface area. Power generating systems would scale with the power generated (the overhead becomes insignificant at this scale), so they would be fine.
I might be overestimating the scaling issue, though. Even without chain reactions neutrons released by fission would occasionally hit other nuclei. So the rate of fission would almost certainly be higher than the normal half-lifes would suggest.
So these RTGs would not be so much devices or even installations as they would be artificial geology in (more or less) state of equilibrium. With a small building (or several) on top to house the actual generators.
So both the RTGs and the fuel contained, essentially large chunks of solid metal, would be stable and secure for probably few centuries, possibly millennia. You can ignore toxicity.
The issue is the economics of something that large and with that long lifespan. I have no clue how it could be possible. Maybe a society that takes a very long view. Maybe it really works better than I thought it would.
I apologize for not explaining properly. I have no idea how I thought people would get the scale issue when I forget to mention it.