The Kazoku was a peerage with around 1000 families. After WWII the use of peerage titles was abolished, with exception of the imperial family. The Kazoku ended as the official Peerage of the Empire and became an association of families which belonged to the Kazoku.
But of course, like for an example in Austria or in Germany, the former royal and noble families are still very much existing, with or without the use of a title. In my understanding imperial princesses remain princesses indeed when they marry a partner from families belonging to the Kazoku, so not necessarily cousins from other branches of the imperial family. This expectation (to marry a royal or an aristocrat) was pretty general in all Royal Houses until -let us say- the 1960's, when the first, fully accepted, non-noble partners arrived on the royal scene and are now normal in all Royal Houses.
Many of the utmost strict rules ate derived from the Constitution imposed by the USA: for the continuation of the monarchy the strictest possible conditions were written down.
I don’t think it’s correct.
The princesses would retain their membership only if they married member of the Imperial family (princes or miyake), but not if they married kazoku.
Chapter VII, ARTICLE XLIV.—A female member of the Imperial Family who has married a subject shall be excluded from membership in the Imperial Family. However, she may be allowed, by special grace of the Emperor, to retain her title of Imperial Princess or Princess, as the case may be.
https://en.wikisource.org/wiki/Imperial_Household_Law_(1889)
Even before 1889 law existed, take for example, Princess Yoshiko of Arisugawa branch (Arisugawa-no-miya Yoshiko-jō). In 1830, 27-year-old Yoshiko was engaged to Tokugawa Nariaki (of Tokugawa Mito branch). After marriage, she lived a life of a samurai wife (her husband even called her “Yoshiko”). Their oldest (surviving) son was the future Tokugawa Yoshinobu, the last Tokugawa shōgun.
Pre-Meiji, with the exception of Tokugawa clan, I don’t think marriage between princess (especially a naishinnō) and noble were encourage (or ever happened), even if it's the Go-sekke (the five regent houses).
Note:
Chapter VII, ARTICLE XXXIX.—Marriages of members of the Imperial Family shall be restricted to the circle of the family, or to certain noble families specially approved by Imperial orders.
This “certain noble families” means the Go-sekke: Konoe, Takatsukasa, Kujō, Ichijō, and Nijō. If you notice, almost every empress consorts were Konoe, while other (past) imperial princes if not marrying cousins they’d marry someone from that clan.
Are the Imperial Family really the only ones in all of Japan who are referred to formally as "-sama"?
No. You can refer anyone with –sama, particularly someone you respect or revere highly (a hardcore fan often refers their idol with –sama).
Komuro's NY bar exam results aren't released and the money dispute does not seem to be resolved, I do not understand why the Kunaicho has precipitated the marriage now when the couple does not yet have a stable situation in NY ?
I can think of only one reason why the Imperial Agency precipitated the marriage : the government plans to reform the rules of succession by letting women remain in the imperial family even after marriage and it was out of the question to let Komuro integrate the imperial family. So they forced Mako’s departure before the reforms
Aiko, Kako and their cousins are therefore “condemned” to stay, Mako is saved
You might be on to something there, Kuro-san.