Whether a rough cut 1x10 was exactly a full 10 inches after cutting (no kerf allowance), or whether that 1x10 was slightly smaller than 10" (with an allowance for the kerf loss) isn't something that is easy prove.
My bottom line: the 9 5/8" hive body depth was chosen because that was a depth that could consistently, conveniently, and economically be constructed from the 1x10 lumber available at that time.
As someone who pulled a pit saw for 5 years I can attest as to how 18th and early 19th century lumber was produced. A line was scribed on the end of a log using a plumb bob as a guide for the square and then another linbe was scribed on the other end of the log and then another line 1" or whatever thickness of board one wanted was also scribed and so on across the one end and the other end. Then a chalk line was laid down the length of the log as a guide for the sawyer to follow. So, a one inch board never has been full thickness, unless kerf was allowed for.
Milled lumber when mills were first set up to mill lumber followed the lead of pit sawing by mimicing the up and down stroke of a narrow blade, one blade at first and then multiple parallel blades in the same frame or sash, thus sash sawn lumber was made.
Then, years later, eventually being able to make a large flat disc w/ teeth that could be sharpened was developed and we got the circular saw. The boards in my house were not cut w/ a circular saw, here in northern NY back in the 1860s. One can see the saw marks on the exposed boards. They were cut w/ a sash saw.
But, like what was pointed out, unless the kerf was taken into consideration in the rough cutting process one will not have full size lumber. And as someone who worked in the 18th century and has worked around modern though old , mostly Amish run, saw mills, the Miller is going to sell you the saw dust whether you take it w/you when you pick up your lumber or not. Understand?
You don't just pay for what you buy, you pay for the production too. That is true in all transactions, I garontee.