I don't have a swivel on my anchor. I've heard that they are week spot and could fail. I've never had any issue with twisted chain.
You are correct, most swivels out there are weak and this is why I pointed to the Mantus unit which claims to be stronger than the chain it is attached to. You may not think you have a twist problem because neither did I until I had to remove all the chain that was on there to remove and perform a full service of my windlass. I have 200' of chain and the previous owner had no swivel installed. The 50'-70' I normally used was twist free because the swivel I installed cleaned it up. Problem was the balance, not that I counted the twists but easily in excess of 50. It is now all cleared up and suspect the swivel will prevent any further twisting. Also I cut off about 75' as in my application I will never use 200. Also found Carver or however installed it, never attached the end of the chain to anything which I did just in case all is let out.
One day if you require to let out more than usual you may be surprised it will stop because there is so much twist in the anchor locker. Just another thing one should clean up and keep an eye on in the endless preventative maintenance found in our beloved past time.