you don't need that kind of precision.
Then why do you specify 16 bit?
That's just plain and unneeded overhead then.
resistors from the same batch are precise enough to be used for such a purpose (try testing them with a good multimeter and see for yourself)
Oh well, did that numerous times over the years and there's quite a variance.
But anyway, let's say you use something like a BK Precision 2831D, a 4½ digit meter (at more than $300, way out of reach of the average hobbyist), you get a precision in the resistance ranges of +/-(0.2% + 6 digits) - assuming that it is recently calibrated
A 10k resistor measuring 10.000 on the kOhm scale will then be between 9,974 Ohm and 10,026 Ohm, ie. a tolerance of +/- 0.26% or 0.52%
In other words, a precision that can be handled in 7.6 bits, so 8 bits is ample
Besides, if you ever tried it, you would know - there's a reason you pay good money for a 16 bit converter
8 bit is fine for some stuff, but it's not fine for music. For example, in a drumbeat, you need crashes and cymbals, which are white noise with a timbre, so to say. With only 8 bits of resolution, a cymbal will sound very bad - try it.
Been there, done that, got that T-shirt decades ago. And... Being an ee with experience from pro broadcasting as well as audiology, I sort of know a wee bit about dynamic range (DR) - but go ahead with your home made 16 bit (or even 8 bit) R/2R converter and get some experience in inferior sound yourself
Btw. Do you know the DR of your hearing? (Hint: Unless you've been tested at a clinic in a sound proofed box by an audiologist recently, the answer is no).
The module in question (why does people call extension modules for shields nowadays? A shield has a very different meaning for me) is ment for a certain kind of apps. which doesn't include 7.1 surround on a $10k+ set up, but rather an easy to use sound clip player for automation projects and similar.
This wave shield is interesting. The sampling frequency is kind of misleading though: is the 20k the sampling frequency (meaning a max of 10k - thus, not very different from ISD chips, which adafruit bashes) or is the 20k the max rendered frequency (and thus, the sampling frequency is 40k ) ?
Even if it was the sample freq. it would be much more versatile than the ISD chips (number of sound clips, possible length of sound clips and with extra SD cards, you can have limitless clips) - whether the sound quality would be better depends on the hardware and how it's designed - like cheap MP3 players that sounds horrible, even if the files are of the best quality.
As far as I read it, it's the max. useable frequency though.