Additional info based on Zhexos's reply:

N.B. There seems to be an assumption that this is only for CPU's older than 10 years old. As outlined above, my CPU is less than 3 years old, so I highly doubt this is the case.

What are your Character and Object Quantity current set to?
Normal
What other applications do you have running in the background while playing FFXIV?
By default I have Discord, MS Edge, and Omen Gaming Hub running, but I've also tried closing these apps and the issue persists.
Is your audio device set as the Default Device? (Yes/No)
Yes
Would the issue persist when playing the game in DirectX 9?
As explained above, it does reduce the sound issue but at the expense of severely bad graphics and frame drops.
If you use a gamepad, does the issue persist when you unplug the gamepad? (Yes/No)
Yes
Does the issue persist when you have the in-game Equalizer Mode set to Standard? (Yes/No)
Yes
Does the issue persist when the Listening Position is set closer to the Character? (Yes/No)
Yes
Please copy/paste your system information.
Already present above!