@Brendan Burgess
A number of different arguments are in danger of being conflated, and possibly confused. Neither of us want that.
I'll try to take them one by one. May not have the time to deal with all of them now, but I'll do my best.
So, what you mean by "emergency measures" is the government stealing people's money. Stealing is stealing, no matter who does it and where they take it from. Are you saying that it's different to steal it from an AE account than, say, from someone's post office savings account? A variation on that is that you're saying it might be easier to steal it from an AE account where the returns are smoothed, particularly if the market value exceeds the smoothed value, presumably on the argument that people won't know the money is missing. What I'm trying to make clear is that everyone will know the smoothed value of their account at any time. The market value can also be easily obtained. If money is taken from the account, both the market value and the smoothed value will fall.
I think you're confused by memories of what happened with the NPRF. There, the government just took the money (I'm sure they described it differently). However, that money wasn't allocated to individuals. A senior Civil Servant who was closely involved with the NPRF told me once that the government would never have dared taking the money if it had been allocated to individuals. Then it would be clear that it was theft.
In future, if you want to mention "emergency measures" as a threat to an AE scheme (whether returns are smoothed or not), it might be best to make your meaning clear by calling it theft. Don't mince your words.
As to the risk of government being on the hook if smoothed value exceeds market value, there is no risk. The smoothing formula is constantly pulling smoothed value towards market value (not vice versa, as some people claim that I'm saying). Therefore, the two will always return to balance. That balance will be restored quickly when cash flows are strongly positive. The example in the paper shows them returning to balance within two or three months even after a massive 15% fall in March 2020, assuming a scheme start date of 1 January 2020. The return to balance will be slower when cash flows are not so strongly positive, or are negative (expected to happen sometime after year 30), but balance will always be restored. Therefore, there is no risk of government being on the hook.
There is the problem, of course, that circumstances would arise where smoothed returns will be lower than market returns for a prolonged period, possibly extending for more than a year or two. One key objection, which I recognise as valid, is that this could cause members to lose faith in the scheme. I don't think it will, partly for the obvious reason that members of the smoothed scheme will be doing far better in such circumstances than members in schemes where returns are not smoothed, and the iron law that returns from risky assets will trump returns from "safe" assets in the long-term will deliver salvation eventually. The paper even shows that to be true for Japan post 1990. After 30 years, the Japanese stock market (with dividends reinvested) was 18% below its level 30 years previously, yet an AE contributor would have got an average positive return of around 2% a year over the period. That's far more than they would have got from Japanese bank accounts. Why? Because their funds were being invested in the market all the way through, when markets fell to the depths and then when they started to recover. The Japanese experience post 1990 is about as bas as it could ever get.
I'll take another look at all your arguments and come back if there are more that I haven't answered.