Anchor swivels, yes or no ?

Absolutely! More so in the Pacific Northwest, as the tides will spin you in circles several times in a day.
Just make sure they are spec'd to match the ground tackle.

Absolutely yes, it helps the anchor dig itself quicker, deeper, and better especially in case of rediging

I've seen a couple of the newer designs fail pretty severely. The older galvanized closed loops stand up pretty well.

My son will not sell the newer design at his marina. The local TowboatUS berths at his place and he has gotten some pretty good work out of these new design swivels.

They're not easy to find, but ABS (American Bureau of Shipping) approved swivels are available. In order to be approved, the entire manufacturing process is scrutinized by class.

I've been recommending the Ultra Swivels for a while now for cruising. The users and customers around me that use it swear by it.
I'm sure it's not ABS or any cert from anybody but never heard of one failing.
http://www.quickline.us/ultra-swivel.aspx

On the other hand, When I set my storm anchors, I make rigs with lots of chain, super long splices, big A thimbles and no swivel.

I really don't see how a swivel will help the anchor set...

On the boat I run, I don't use one and anchor probably 100 to 150 times a year. Never needed one. Don't have one on my hatt either.

The biggest benefit is that you don't have a shackle pin catching the edge of the roller frame which is one I put on Kong swivel on my small gaffer.

The Kong is supposed to be really good. A few years ago I left a 110 lbs Bruce in the bottom of the Indian River off Titusville Fl when the Suncor swivel failed while setting, thankfully those Bruce are cheap!

Never used a swivel, anchored more times that God.
Never had a problem.
(Caribe, Bahamas, Florida, mostly shallow stuff)
It may be different in the Pacific NW and other areas.
Afraid of internal corrosion with subsequent failure.
Used to be a young live-board with no insurance.
No swivel, just big anchor, big chain and slept with an eye open.

I don't think that I have worked on a boat that doesn't use them but we are all chain. I won't be using one on my own smaller boat with a mixture of chain and rope anchor rode.

God doesn't anchor. She has DPS.

Check into my post #6 above.

Hmm, I googled DPS and none the wiser.
Is God a Shemale?

Dynamic Positioning System.

Dags Private System?

Funny Belle!

Back in the 70s and 80s we anchored 25 times a day in water depths from 30 >300 ft for 9 months a year for 3 years. With 3 strand nylon we had to use a swivel to prevent hockels with braid we didn't. we used a hammerlock swivel hammerlock then the anchor on a 80kg danforth style on a 100 ton vessel

But of course. It came pretty far down on The Google list
However.

Heard of some helicopters having a similar system, you can park them in the sky and they will maintain position.

What may I ask were you doing that required you to anchor every 57 minutes?

Most harbors on the great lakes have a river that has industry or agriculture that add (stuff) to the lake, In 1975 for example we did a grid with 21 stations from the harbor entrance out to 100 meters and and on each side, at the mouths of Ludington MI, Manitowac WI,Racine WI,Port Washington WI,Grand Haven MI,Waukegon ILL, Michigan City IN,Benton Harbor MI, South Haven MI,Holland MI, Grand Haven MI , Muskegon Mi, and back to Ludington MI. We did this continually from april thru november at each station we would collect a bathythermagraph 0f water temp a transmissometer of water clarity water samples for coloform bacteria,dissolved oxygen, bottom samples,net tows for phyto and zooplankton,and water samples for trace metal analysis.