One additive I am convinced helped me and everyone who I recommended it to who actually used it claimed they really appreciated the difference it made. The product is called "Restore." It is for well worn engines. I would never put in in an engine unless it has better than say 125,000 miles on it. I would not put it in the engine of something really valuable either.
One other additive I think helped me on my ST1100 motorcycle is called "Sea Foam." It seemed to make it much easier to start, and also made it idle better. I don't ride it as often as I should. It has around 65,000 miles on it.
I know certain additives can swell rubber a tiny bit and make a seal quit leaking for a while. (I work in the rubber industry.)
But, none of these engines were new. One problem with an additive is that you have to have a problem that additive can target, and it has to be relatively mild.
Subaru requires a a leak stop additive made in England be added to all Subarus else you void the cooling system warranty.
I know it will be a bit hard to swallow for some of you guys. All I can say is that I am not a flighty person, and I do not subscribe to a lot of voodoo.
As for oil analysis: I find that analysis of oil is in direct proportion to mostly the cost/value of the equipment. Our tiny boxes are never sampled. Our gearboxes from $75,000 to $250,000 are analyzed at least yearly, along with the vibration analysis, and in some cases thermography studies.