I’m using an RME ADI-2 DAC and Volumio on a ZeroW. I’m hearing faint pops and clicks in the audio. It happens in SpotifyConnect and Airplay, but not really when playing local files. The pops seems especially frequent while Volumio is indexing new files, so I’m wondering if its simply a processing or throughput bottleneck with the Zero. Am I expecting too much out of a $5 computer attached to a $1000 DAC? Should I go buy a Pi3?
Yes, good USB performance from the Pi Zero is expecting to much 
Get the new Pi 3+ which has much better performance especially on the USB throughput and interrupt handling.
Its a very small investment (35$) compared to your DAC.
Also consider getting a good (Lineair) powersupply and an usb filter, both not big investments compared to your dac (maybe around 150-200$ total). That way your 1000$ investment in your DAC actually performs to its value.
Poluted power also polutes your DAC signal and affects your DACs output.
Btw: I assume that your DAC is self-powered and not via USB and also has its own clocks to reclock the ‘badly’ timed USB signal
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Hum…could very well be wifi limitation rather than USB (though all Pis have USB limitations). You may want to characterize the issue more precisely.
Built-in wifi does not have a big antenna, so you might have poor reception.
You could test throughput with iperf for instance, and check if a USB wifi dongle (wifi or ethernet) won’t give better result.
Also, do you have dropouts if files are on a USB disk (you mentioned internal files, assuming you meant on-SD files)?
If you have a good quality powered USB Hub, you may also want to give it a try as Pi might be limited in driving enough current on USB for various peripherals.
The RME DAC comes with its own suite of test WAVs, and when played from the Volumio SD card, the DAC confirms bit-perfect playback from the PiZero up to 32bit at 192k. I’m not sure how much better than “perfect” I could get with “usb conditioning.” The RME has exemplary data reclocking and internal power filtering.
I found a Pi3 and booted the same SD card. No more pops and clicks on Spotify Connect. It seems my suspicions were true and it was a CPU bottleneck.
Well,… no issue with Pi3, but issue with PiZW is the only thing you can conclude at this point…
May very-well be sufficient conclusion for your daily operations still.
To investigate actual reasons (CPU, memory, network bandwidth,…) you would need to do more technical diagnostics (provide logs, look at top figures under ssh, etc… on both devices during bottlenecks, etc…): there are far too many “moving parts” still.
Recent kernel (4.14.x) also comes with unresolved issues, currently impacting differently various Pi devices, etc…
It would be interesting to find-out and see potential SW fixes if any (for instance we know currently-used MPD version has under-run bugs), as PiZ devices are often capable enough for “simple” music streaming (audio-processing like resampling/post-processing might sometimes push it too much).
So if interested in figuring-this out, feel free to post more details.
If not, just enjoy your setup! 
PS: I’ve been doing Spotify connect with my 2 PiZero just fine for months.