What bothers the Conservatives is not to have a reigning empress but to have these children succeed her because it means a change of dynasty if this empress marries a commoner.
I read an article not long ago that several members of the LDP (Liberal Democratic Party in power of Prime Minister Shinzo Abe) were planning to draft a bill to allow unmarried men from former imperial branches (Ōke) to return to imperial status by adoption or marriage. And I even read in this article that there would be 7 single men in these former imperial branches: 5 teenagers and 2 in their early twenties. So yes, these collateral branches do have male heirs, and very young.
Princesses Akiko (38), Yoko (36) and Tsuguko (34) are far too old to marry such young cousins, the age gap is far too big.
Princess Mako (28) is already engaged in a relationship with Kei Komuro but since the controversy over the financial problems faced by the Komuro family that led to the postponement of their marriage in 2020, we do not know whether this marriage will take place or not. Princess Mako is approaching her 30s, so again, the age gap is significant.
Princess Kako (25 years old) is still well into her twenties, it remains possible but well, I doubt it will be done.
Princess Aiko, 18 years old, is the only one who has an appropriate age to marry one of her cousins.
If Aiko marries one of her cousins from the collateral branches, she can rule because her husband is a member of the imperial family, he has just been reinstated so there will be no dynasty change, it is not a commoner and then Aiko is the only child of the Emperor and it is better to follow the direct line of succession (unlike Hisahito). And their children can succeed their mother because their father (Aiko’s cousin). But this does not guarantee stability, because if the couple does not have children or boys afterwards: still a dead end. And if they only have daughters, they will have to marry a cousin to succeed their mother?
So it is not a lasting solution but this marriage can be a good compromise: the conservatives will agree because there will be no dynasty change on the throne and the progressives who support an egalitarian succession will also be. I think that can be a good start towards the total change of succession rules, Japan is not ready for that yet. And then Shinzo Abe will not be Prime Minister forever, he will leave power in September 2021 and the ceremony of proclamation of the crown prince Akishino is postponed, maybe even that it will be until then?
Personally, I hope that the Emperor himself will leave his right of reservation on the question, the only way to get public opinion to react and to push the Prime Minister to change the rules. I do not know the opinion of the Emperor, but we are still talking about his family and his dynasty, and to continue with the current rules will only participate in the extinction of the imperial family. (sorry for my bad english)
Article (in japanese) :
https://www.sankei.com/life/news/191028/lif1910280004-n1.html