I remember when SGI (Silicon Graphics) paid a bunch of money to rebrand to . . . drumroll . . . SGI! The consultants must have been high-fiving each other after that one landed, it's like trading in your car only to find that the saleswoman has sold you your own car back, at a profit. (SGI later collapsed due to "Corporate Campus Syndrome", and other companies, including Google, now occupy the wacky buildings they sp…
That said, SGI had an iconic logo of a cube formed from a single periodic pipe before. I was using SGIs daily at the time and I almost cried when they did the rebrand.
The rebrand replaced it with a contemporary (at the time, mind you) typography logo that would look outdated if the compamy still existed.
To their credit, the rebrand did include a typeface design for use with all their design, i.e. detached from the logo.
The resp. fonts would have the aforementioned issues though -- one variant was used for the logo which is kinda cheap.
But at least they had a tyepface designed and it was recognizable. That rarely happens. Commonly a rebrand will just swap the old typeface for something different but already existing.