Indeed, these have a PLL (some with ASRC, like the ES9038). I didn't even know the PCM5102A had a PLL, thanks for pointing that out

But this is in no way common. DACs like AK4493Q (and others from the same series) do not have PLLs. Neither does the Ti PCM1795, nor the Cirrus AD1938, for instance. So it's quite a mixed bag.
Now, one could simply say: use one of the ones with a PLL for now

. That would save time implementing a more advanced clocking system and spend it on more interesting features
You can get a PCM5102A board for under €$ 2 at AliExpress, an ES9018K2M for below € 12... (just don't blame me when they are fake
)
So you can effectively make an 8-channel DSP-enabled DAC with a 100+ SINAD for way under €$ 100 (or even under €$ 30 if you use the PCM), including PSU and a halfway decent enclosure. Amazing times!