Emperor Hirohito was forced to renounce his claim to divine status...but he still technically claimed divine descent.
The Americans forced Hirohito to renounce his "divine" nature, however they made a huge mistake about it.
Basically, what happened was the Allies were looking at it from a strictly judeo-christian understanding of what a "god" is and made the emperor denounce a kind of divinity he never claimed to have in the first place - namely that of being an all-knowing, all-powerful god.
In his humanity declaration he used a certain term, namely that of
akitsukikami (which could be translated as "Manifested God") rather than the term
arahitogami ("Living God"), however the official english translation only uses the term "divinity". The difference between the two terms, however, is rather large in Shinto understanding.
mostly because the many religious rituals they had to do were so tedious and repetitive that even Japanese people thought "fuck this shit"
Resigning freed the emperor of certain time consuming duties and court ceremonies as you said, but that meant that he wasn't tied down by court restrictions and thus could move more freely and better wield his power.
Granted this was only relevant at certain times, seeing how the emperor was divorced from power for centuries at a time.
Later, abdication was a tool to put more desirable people on the throne (such as Taira Kiyomori making his nephew the new Emperor).
I wouldn't be surprised if many of the tasks the Emperor has were invented specifically to tie him up in court procedures and ceremonies in order to hinder his ability to put any kind of resistance towards the military rule.
Personally, I've always thought "Pope" was a better translation for 天皇 (Tennou) than "Emperor" since "Heavenly Sovereign" is the literal translation of that title, His Holiness is technically a monarch anyway, and the role has always had a stronger religious component than political even at the respective heights of their powers. I just never knew this was official.
Only when you have a certain distinction between "heaven" and "earth".
~1500 Years ago, some clan managed to overpower the surrounding clans and ruled over a larger area than all the people before him in Japan. In a rather smart move, they declared Amaterasu (the goddess they claim as an ancestor) the supreme goddess to legitmate their reign. Fast forward a couple hundred years and these people suddenly live in a world of poems, music and parties at their court and have to rely on their warrior subordinates to retain their power.
However the military leaders eventually realized that they can be the de facto rulers but rather than overthrowing the Emperor, they keep him as legitimization for their own power (as that particular part of the imperial bloodline was a very good institution to avoid usurpers).
Thus, the imperial family was now a token to make ones rule as regent or general (more) official.
Strangely enough, the very same developement threatened Shoguns as well, making their clans figureheads while yet other people ruled through
them.