JimD is quite correct.
The EROEI calculations that show high numbers are invalid. 2 is a more reasonable estimate. And that is based on light water reactors using uranium from another era. Uranium prices now are highly biased by the conversion of weapons enriched uranium and naval nuclear fuel uranium to low enrichment nuclear fuel. The immense energy required to perform that original enrichment is excluded from the calculations resulting in an over estimate of the EROEI.
Molten salt reactors have much less data. And they are by no means a panacea. They come in several varieties. The most commonly proposed is based on previous reactors and involves using a salt that is made up of sodium, potassium, lithium, beryllium and other fluorides. Notable is the inclusion of the beryllium - an exquisitely toxic and nasty element.
And the most commonly proposed versions are based off of thorium - uranium-235 blends to start. As the reactors age, the thorium is bred into uranium-233. The idea being that in time the reactors become a fully closed thorium-U-233 cycle.
However, the fission product wastes must still be felt with. It isn't as simple as taking them out in the salt and disposing of the whole lot. That idea is part and parcel of the ideas that have gotten us where we are. i.e. dig stuff up, process it to what we want, then throw it "away". There is no place called away in the real world. Whatever we make we are stuck with. Most often the titans of industry and government conclude that somewhere far from most people is a perfectly fine place to put poison that they don't want anymore. In reality, the best place to put waste and poison is right in the middle of the largest population centers. The proximity forces them to deal with the problem, and in the end to choose to not create the waste in the first place, or to reclaim, reuse and recycle it in benign ways. Nuclear fits none of those options.
Worse yet, proposals and tests that electrolyze the salt to separate the uranium, plutonium and thorium from the fission products are immense proliferation risks.
At the end of the operating cycles for nuclear fuel, there are several left overs.
First - intensely radioactive nuclear fission products. These must be isolated and secured for thousands of generations.
Second - thorium and uranium that was not consumed. The isotopic are now different and become a real problem for reusing or recycling any of it. That and contamination with other elements make reuse extremely ineffective and drive the EROEI below 1 for the whole system. This is true whether the product is from a molten salt reactor, a light water reactor, weapons plutonium converted to mixed oxide fuel, or any other. So reuse as any sort of practical matter is out. Also, the neutronics of the reactors based on these recycled fuels in addition to being non cost effective make them vastly more dangerous. They operate far closer to the edge of disaster.
Third - a whole bunch of actinides have grown in. These are immensely dangerous, hard to handle, harder yet to separate from the desired isotopes, and progressively harder to burn up. Many of these are extremely long lived hazards that are even harder to deal with than the spent fuel or the fission products.
Fourth - there are a bunch of light elements to deal with, including tritium, carbon-14, radioactive iodine and others. The industry would very much like to hand wave these away and simple let them blow away not he wind, as yet another externality. In the case of the vitrification plant at Hanford, the original design failed to include any means to capture radioactive carbon-14 emissions from the glass furnaces. And there is a lot of it.
Fifth - there is a lot of neutron embrittled and now radioactive metal. Ideally that would be recycled back into alloys for the reactor industry. But they don't want it any more than anyone else does. It is too hard, too expensive and too dangerous to handle and reuse. Again though, the industry would like to minimize the risks and sell the contaminated metal into the marketplace (especially the nickel from the centrifuges).
Sixth - there is a mountain of lesser contaminated wastes that must be isolated for long periods. These include the bulk of the facility itself.
Seventh - the molten salt reactors are vastly more susceptible to diversion of fissile materials for nuclear weapons use in the form of very high purity uranium-233. U-233 that is very low in U-232 is just about the most ideal nuclear material for a nuclear bomb. Plutonium weapons can be somewhat smaller. U-233 weapons can be vastly simpler.
Eight - worse yet is that uranium forms two stable fluorides, UF4 and UF6. In one of the previous molten salt reactors, no one noticed until decades after it was shut down that U-233 had accumulated to serious concentrations in a side leg, levels that could easily in a power rector become an uncontrolled and uncontrollable criticality hazard. Knowing that now, that can be designed out. However, it points out a fundamental issue that was not recognized and that must be dealt with.
Ninth - in the event of an accident, the molten salt reactors have hazards vastly different from the light water reactors. The designers of several types of light water and plutonium reactors were absolutely nothing could go wrong with them creating severe accidents. They were wrong. There is no reason to believe that molten salt reactors don't also have hidden severe hazards. It is in the nature of high energy density sources that such things exist.
And these facilities like any other have life spans. At the end of those they cannot simply keep being extended. They wear out. In part that life was determined by cost considerations when they were built that caused the designers to go cheap in the designs. Doing things better to allow longer life costs more and also reduces the EROEI.
And all of this excludes the immense energy externalities involved in the mining, milling, enrichment, fabrication, transport, construction, demolition, transport again, and disposal of all of the things that go into building these plants.
They also cannot be run as other than caseload. They do not do well with cycling power levels. Doing that drives the EROEI to well below 1. And for economy reasons they must be large. Periodically these very large power plants that form the backbone of a network must be taken off line for maintenance (or emergencies). When that happens, there has to be enough spare capacity to replace them. But none of that gets added into the energy costs of these brutes.
Nuclear is seductive because of its extremely how power densities and its seeming quietness and cleanliness while operating. But this is a tiny time slice in their life and excludes the bad bits. The power density though is the single largest draws.
Having personally run a nuclear plant, and having personally been showered in primary coolant, and breathed carbon-14 dust, and handled nuclear wastes, and worked with them and everything that goes into handling them, I have a pretty good idea of what is involved.
The plants running today have severe flaws. Some are running that frankly should not be. Some have broken support brackets for internal electro pumps. Some have fractured control rod drive sleeves. Some have leaking primaries. Many have leaking steam generators. Many have fire hazards that jeopardize the controls. Many have ancient control systems with failing components for which no spare parts have been made in decades. Their control systems are ancient and retrofitting those is no trivial task. Most have severe radiation induced concrete damage and are wholly unaware of it. Worse than all of this, they are getting very very old.
In an ideal world where minimum cost wasn't the deciding factor and where people understood risk and consequence management well, nuclear might have been useful. We don't live in that world.
The numbers of reactors required, the pace at which they would have to be built, and the issues with fuel, recycling, wastes and accidents each and all render nuclear as nonviable in the fight against climate change. They are at best a distraction from doing the real work.
And if all of that isn't bad enough, the world is awash in weapons usable plutonium from weapons production, from nuclear fuel recycling and from spent nuclear fuel. As this ages, difficult isotopes decay away first leaving plutonium and uranium that is vastly easier and simpler to use in nuclear weapons. That "little" problem with be with use for a million years or more.
As to the costs estimates from DOE. The reason for the sudden rise is that they were dramatically low balling the estimates from the time they first prepared them. They have now had to become more honest about the costs. They still haven't come to grips with the whole cost, either in dollars, or in non innumerable costs (environmental and human health particularly).
As to the science issues. This is boogey man proposed by proponents. The problem is not that people who oppose nuclear power don't understand that realities or the science. The problem (for the industry) is that they do.
Sam