What "duties" does good 'ol Aki even have in the modern day?
Plus, wouldn't this make the presumptive heir either a woman (if they pass a law allowing Aiko to take the throne) or a little boy?
Some representative functions aside he's actually important for religious stuff. To put it bluntly, he's to Shinto what the pope is to catholicism and has to do various ceremonies on a regular (ie: not just annual) basis.
He's also kind of the "supreme father" to all japanese families, a living god and the symbol of unity to japanese society. His actual political power is limited, but his influence on certain aspects of society are strong. So if the emperor was strongly in favor of a historical reconciliation with former victims of japanese imperialism, it would actually force the japanese government to act accordingly.
In terms of the heir, that's kind of an issue the imperial Palace has had for decades. Unlike in (say) England, where there's the Queen, in Japan having a female heir is practically unheard of. There have been certain women who were Empress, however they always became that through marriage and only took over the power once their husbands died (and even then, there have been regents). So while there's precedences for Empresses, they aren't really relevant to the issue of the heir. On the other hand, primogenitur isn't that big a deal in Japan as it is in other monarchies, so they could make Fumihito the next emperor, however his idea of being Emperor is basically waving at people and doing what he's told, while his older brother (the current heir) has a much more proactive understanding what an emperor should be like.
The emperor not being able to abdicate is actually a remnant of the Meiji Constitution of the late 19th century where certain people pretended to put the Emperor in charge but actually kept the power to themselves. In order to further divorce the Emperor from power, they made it impossible to abdicate - which had been exceedingly common in the past to a point where the abdicated Emperor usually was more powerful than the one that was officially in charge.
A possible solution might be for Naruhito to simply adopt his younger brother's son, still, the japanese royal family is kinda dangling above a chasm. If this son of Fumihito doesn't produce a shitton of possible heirs, we might see the death of the japanese imperial line.
The US ensured that the emperor was deranged during Japanese occupation, so this will have no effect on the day to day life of the average person in Japan.
That's what people thought back in 1988 before Hirohito died and japanese society went bonkers the moment Hirohito was dead.
I mean, sure, they won't go crazy over their Emperor abdicating, but the fact this information had been first leaked to korean newspapers (if I recall correctly) is rather telling. Basically, as long as it's an unfounded rumor originating from the outside, the imperial palace can gouge the population's reaction and opinion and then either deny or confirm it.
Japan was rather supportive, therefore they now make it kinda-sorta official.
Though they have to change the consititutuion first, and that's kind of a bother, since everything involving the constitution and the Emperor is always bound to raise some eyebrows among japanese neighbors.
