The harddisks should be spinning down when not in use. If they're not spinning down, that's the problem he should go after.
Plus, if they're actually loud, then he has crappy mounts and a crappier case.
I have a Synology NAS that was silent, but recently upgraded the HDDs to Toshiba NAS drives as they're very well regarded by backblaze and reviews. But they are noisy, the chunking sounds of seeks is audible almost throughout my apartment, the case and mounting is just fine thank you, sometimes the drive models are just very noisy and the environment is just very quiet.
For me it's fine, it's just a new sound in the background along with the hum of the fridge and gentle clicking of the boiler coming on and off, and yes my drivers stop spinning when not in use (but I share my Plex with my partner who listens to our music at her work).
At the moment, I SSH from my phone to a Raspberry Pi in order to WOL the NAS when required. It has the appropriate power settings to spin down and then switch off after a period of inactivity.
Coming to think of it, at some point I may have implemented a single button wake (like the article) by creating a JuiceSSH profile to run my WOL bash function then exit as a snippet, and then making an Android widget on the homescreen to connect with that profile. Probably deleted it because I kept accidentally pressing it :-/
I have something like that as a termux shortcut and it works nicely ( https://wiki.termux.com/wiki/Termux:Widget ). Pretty simple, too; just stick the ssh one-liner in a script in ~/.shortcuts/ and it works.