First, I want to make it clear that my claims are about relative subsidy, rather than absolute subsidy.
Second, the nuclear insurance subsidy is not really a subsidy, since the taxpayer is only on the hook in the case of an accident, which is not only extraordinarily unlikely, but also mitigated many times over. The calculation of the implicit subsidy to nuclear power comes from highly motivated speculative accounting by CATO, whom you should generally think of as playing the role of a law firm working for oil and gas and against alternative forms of energy production. There are a range of values which could be assigned to the "implicit subsidy of nuclear insurance", and the opposition lawyer has obviously chosen the absolute highest end of that range.
It is difficult enough to calculate the probability of a nuclear reactor meltdown, but we have observational evidence that it is at least many dozens of times less likely than say, a hurricane, and each of those is generally more costly than even the worst nuclear disaster in history. The damage wrought by the tsunami at fukushima, for instance, was many times greater than the damage wrought by the meltdown at fukushima.
There is a private component to nuclear insurance, as well, paid by the operators, which totals, across all nuclear plants, approximately 10 times the total damages incurred by the three mile island incident every year. It is extremely unlikely that a nuclear accident will ever exceed these damages.
This is in stark contrast to other historical insurance requirements. As a case study, I recommend learning about the early history of oil spills starting with the https://en.wikipedia.org/wiki/SS_Torrey_Canyon and the subsequent founding of TOVALOP in 1968. Up until that point, oil transport insurance was implicitly subsidized by the nature of a limited liability corporation. Note that this was not an artefact of the times, since insurance requirements for the nuclear industry were implemented by congress a decade earlier, in 1957.
On the other hand, we subsidize coal and natural gas implicitly by not charging them for the use of their exhaust channels and also not structurally supporting torts for worse health outcomes with no easily identified proximate cause. For a concrete example, I think we have a pretty good idea of the number of additional hurricanes per year we can expect as a result of carbon dioxide emissions, but we do not require oil and gas to pay for marginal additional hurricane insurance, despite that doing demonstrably more damage than even very bad nuclear meltdowns. The unsuitability of tort as an avenue of collecting externalities is an enormous implicit subsidy for the fossil fuel industry.