I think your expectation of "very, very slight differences" between the registers breaks down in the extreme situation where almost all the finger holes are covered, as when playing the lowest three notes (B C and C#). Opening the top hole to suppress the fundamental tone relies on that hole being at the correct acoustical position along the pipe. That position is inevitably a compromise, and it is chosen to work well for higher notes. In effect, the standard fingerings for the "upper register" C and C# are really creating a very short length of pipe sounding its lower register.
There is no logical reason why a wind instrument must necessarily switch to overblowing at the octave "just because you can," though of course human anatomy imposes practical limitations on the number and position of the holes which limits the useful compass of the instrument without overblowing.
"Capped reed" instruments (crummhorns, bagpipes, etc) which can't be overblown at all, often have a compass of a 9th or a 10th rather than an octave, using the same basic idea to get the highest notes.
The recorder family follows a similar fingering system to the flute - the "obvious" pattern for fingering the second octave doesn't begin until a few semitones above the octave of the lowest note.
You might like to explore the "virtual flute" at https://newt.phys.unsw.edu.au/jw/virtual.html - which gives no fewer than 666 alternative fingerings for notes "close to" the upper register C, for example.