if voters and politicians are acting in their self-interest, we should expect that politics as a whole has a shorter time horizon than if younger people were more empowered.
This post's argument seems to rely pretty heavily on the assumption that people vote in their self-interest. Yet, as you note, "in general, voting behaviour isn’t well-explained by the ‘self-interested voter’ model." For other readers interested in this debate I'd suggest Caplan ((https://en.wikipedia.org/wiki/The_Myth_of_the_Rational_Voter)),
The evidence cited that older generations do vote in their self-interest (looking specifically at cases of direct democracy, which is arguably a somewhat peripheral part of the political systems in questions) seems exceedingly weak compared to the evidence against self-interested voting in general.
For example, it relies on subjectively coding rather broad categories of decision as consistent with narrow self-interest by the elderly, neutral or opposed to narrow self-interest. In most cases (see table 2), this just seems to come down elderly voters being opposed to more spending (except for health). It seems rather speculative to chalk this up to generational self-interest, especially in the face of a lot of evidence that voters are generally not self-interested.
This could be significant. Currently, the median voter is 47.5 years old in the USA; the average age of senators in the USA is 61.8 years.
It's also worth noting explicitly that the dynamics of politicians (potentially) voting in their self-interest should be quite different from ordinary voters (potentially) voting in their self-interest. Certainly a 61.8 year old senator might slightly personally benefit from voting for, say, higher health spending, and thereby be more motivated to do so than a 47.5 year old senator, but it seems like in most cases we would expect these effects to be swamped by other incentives politicians have e.g. maintaining political power.
Imagine, at the limit, someone who was voting on their deathbed. They would only have moral concerns to guide their decision.
I'm not sure if this is of substantive importance to your argument, but this doesn't seem true on either the conception of self-interest typically employed in these debates or the folk concept of self-interest. Even "narrow self-interest" is typically taken to include the interests of one's immediate family/household. It seems like we would typically say that someone who, on their deathbed, acts to ensure that their money to go to their family rather than someone else's family, is acting self-interestedly.
one way of extending political time horizons and increasing is to age-weight votes. The idea is that younger people would get more heavily weighted votes than older people, very roughly in proportion with life expectancy.
I would expect this to have some effects which may be considered deleterious.
For one, it seems like this is not just changing the weighting of the vote, but it's also changing the incentives to vote (and to be politically engaged more broadly) i.e. presumably older generations would be less likely to vote and younger generations more. One might view that as a feature rather than a bug, working in line with the direct effect of the vote weighting (especially since it's the opposite of current trends). However, it would likely also decrease political (and perhaps more broadly, civic) engagement in older generations, including their incentives to engage in political deliberation and debate. This would plausibly have negative effects, both by making the older generations less informed and deliberative (and so plausibly reducing the quality of their vote), but also reducing their input to the deliberative system as a whole.
A further problem is that some evidence suggests that, weighting votes differently (on the presumption that votes reflect individual interests might itself help to create self-interested behaviour that there wasn't before (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.597.7508&rep=rep1&type=pdf)