Does soaking in saltwater for 20 mins help cleanse mussels?
Where I come from (Portugal) it is quite common to see in most restaurants and establishments shellfish being soaked several hours to even days long before consumption, especially sand dwelling shellfish, which is not the particular case of mussels.

The reason for this is that it keeps them alive and fresh for longer, while also purging any remaining sand or debris naturally found inside them, which is very common in burrowing shellfish, quite unpleasant to find when eating and can virtually ruin the dish.

These are however always soaked in either salted tap water at worse, or at preferably clean natural sea water from where they came from at best. Never just unsalted tap water, because this would obviously kill them quickly, and remove any natural salt that acts as flavor enhancer. Chlorine based disinfectants commonly present in tap water will also slowly affect quality of any living creatures (including aquarium fish) and may eventually be fatal them in the long run.

From your provided examples, most against soaking either state that tap water will kill them quickly, or considerably affect quality (which are both true); or is not needed for farmed shellfish.

I can't speak much for farmed shellfish, they are not as common here and quality may vary with providers and techniques, but even farmed one can some times be quite sandy.

So I'd say that soaking with either salted water or ideally sea water is at at worst redundant or not needed, but can be quite beneficial in some situations.

For farmed shellfish, if you find them clean and edible it is probably not needed, for "free range" ones you probably have more to gain by soaking than not.