[edit: I may have, uh, flushed a little soon here on one point: Scott wasn't the later company of the patent holder, the Albany Perforated Wrapping Paper Company was--so Scott may have followed their standard, not vice versa. In either case they shared a form factor, which may be telling.]

I can tell you what predated ASTM standards, and why they exist. It's almost certainly the result of the Scott Paper Company, which was a pioneer in disposable roll paper (patent 1871) [.edit: actually patented by the Wheelers of the later Albany Perforated Wrapping Company, who pioneered perforated paper.] In short, the initial production was from a large 72"-long roll, initially unperforated but later divided into 1,000 sheets; the company sold dispensers as well, and the two needed to work together, as well as hitting the sweet spot for the manufacturing process. The manufacturing process hasn't changed that much, either; if you look at steps 6-10 in this general discussion, you'll see the crepeing and large rolling (before slicing of "logs" into rolls--though I'm not sure how long the long spools were) processes, which at one point would have made both rolled paper towel and toilet paper from the same master rolls. That's not the case now, but the tubes of the two were the same size for that reason. Once Scott [and APW] had proven the market, imitators arose, but they needed to sell for the standard fixture. (The big rolls in institutional use are another category, but the mechanic is probably similar--core size is fairly standard.)

If you look online, you can find antique Scott and other early toilet paper dispensers. The international and other standards today reflect a lot of the legacy of that early sizing for consumer paper rolls. [edit: I've been looking a bit, and this is one example of an early cradle holder, with toothed edge for tearing unperforated rolls. But at around the same time (1880s) were Scott branded placard, wire, and wooden dowel holders too, though I can't find the original of that--but they evidently did patent the design at some point if the wall piece is to be believed. But clearly APW had its own designs that held the paper out from the wall, and at some point used that one too--but these TP holders don't bear dates, sadly.]