* Until 2000, stocks were priced in fractions of a dollar (8ths, 16ths, etc) before moving to cents (https://www.sec.gov/hot/decimal.htm)
* These days, prices on exchanges must be in one cent increments, and not smaller (https://www.sec.gov/divisions/marketreg/subpenny612faq.htm)
Perhaps they're using the same software as for overseas markets, or its some future-proofing gone wrong or something.
For example one can submit a mid-point peg order which can be filled at a fractional penny:
https://www.nasdaqtrader.com/content/productsservices/tradin...
There are also auctions that take place on a daily basis, such as the opening auction and closing auction, where trades may execute at a fractional price.
Furthermore NASDAQ also operates as a reporting facility, and as such reports trades made through ADFs such as FINRA, dark pools, off-exchange block trades, and inside quotes which are quite often executed as fractional pennies.
https://www.nasdaqtrader.com/content/home/help/tsiqtxtkey.pd...
Anyways, all this to say that the situation is a lot more detailed that you make it seem from your two references. It's not just a simple matter of SEC says orders have to be to the penny, so NASDAQ must be doing something really bizarre here.
The rationale and effects of the sub-penny rule are quite complicated. And there's lots of lobbying done in either direction.
The bigger the smallest price increment, the more important speed becomes.
The original justification for minimum increments has gone: it was a workaround the limitations of human traders and human market makers.
But, alas, even with computers there are still some downsides to just allowing essentially arbitrary precision prices.
(I do find it somewhat strange that the SEC makes rules about this, though. Why don't they leave that to the individual exchanges?)
I think we had a discriminant for the denominator, so it wasn't a rational type, but we could also easily represent both fractional and decimal prices. We could handle fractions smaller than 1/16, though I don't know if any equities traded at such prices. What you suggest would also be reasonable, but would have had to be rewritten when decimalization happened.