I believe its the action of unattended consequence. Whilst the intent maybe sea control its ultimately aimed to counter US influence. Until the US is in a position where it can no longer provide the necessary counter balance JPN & SK will not pursue weapons of mass destruction its still a milestone that would take close to a generation to achieve.
On weapon of mass destruction, I believe if need be and 'if' the political will and public support behind it, Japan can reach it much sooner than close a generation time frame. They already have stoke pile of Plutonium, and have technology to weaponise them. For delivery system, their space agency satelite delivery system, is already in advance enough level that change it to MIRV is not big endavour to do.
ROK, will need more effort than Japan to reach it, but considering they have much more resources and technological based then their cousin in North..well if Fat Kim can do it..Seoul can definetely done it much faster than the North if need be.
Still I agree, it will much depend on how both Japan and ROK see US policy on covering nuclear umbrella to them progressing in future.
Back to Izumo, it's very interesting how this will progressing. Izumo already in right size to operate at least a fozen F-35B, and modifying internal infrastructure can be done considering it's already operationally capable for V-22. They do have to add sky jum facilities. However it's very doable, which I believe why China do take alarm on this, cause they knew Japan is in possition to change both Izumo's as CV in relative short period.
For ROK, I do agree with Swerve, Dokdo is too small to be modified for that purpose. However, ROK have enough technology, resources and facilities to lengthen and widen Dokdo design for CV purpose. They will do it, I believe, if Japan decided to modified Izumo's.
As for larger Izumo design, I believe they already have prepared it..if not mistaken on reading some Japanese internet..