I currently rotate chains on only the Brompton because it sees by far the most use.
This wasn't necessarily originally my intention however I bought a second chain for its corrosion resistant properties but found this proved largely irrelvant so just started rotating the two. The modest amount of light surface corrosion encountered with a waxed chain in the wet is neither here nor there in any meaningful sense - either practically or aesthetically; while the corrosion only occurs on wear surfaces so any original anti-corrosion coating gets worn off pretty rapidly in any case.
I rotate for convenience - using the bike multiple, long days consecutively means it's handy to be able to just swap the chain to a fresh one and wax the other at my convenience. It also means I can wax two chains at a time (either both from the Brompton or one of the two along with one from another bike when that needs doing) minimising the time and energy costs.
Waxed spare chains are kept in labelled bags; the bag and chain going loose into a "to be waxed" bag to await the next waxing once removed from the bike.
As I think has been touched on in the past rotating should also prolong the lifespan of the rest of the drivetrain; since elongated chains wear teeth at a faster rate. So in theory running two chains in rotation until they reach their wear limit should cause less wear to the chainring and cassette than running one chain to it's limit, then doing the same with a replacement.
I've considered adding more chains into the mix however have so far resisted on this bike as each has a projected lifespan of around 5k miles at 0.5% wear, while the bike is on about 3.5k miles so the chains have around 6.5k miles / two years left between them at the current rate and I hope to move at some point which will take this bike out of regular service. If life sorts itself out I'd hope that the current chains might last for the remainder of my time using the bike..
I don't currently do enough distance on my other bikes to bother sourcing another chain for rotation. Hopefully if I ever move I'll be using one / more of the other bikes more so it might make more sense then.
Ultimately rotation is good but has practical limits. Generally the more the better; however there's little point dying of old age with 100 very slightly used, near-pristine chains to your name.
Also while I'm all for prolonging everythings' life there becomes a point where this is also less relevant; for example after about 4.5k miles the waxed 11sp chain on my Genesis is suggesting a lifespan of something ridiculous like 50k miles. Assume that the cassette and other bits will require replacement after three chains and that makes it highly likely that I'll never have to replace any other drivetrain components in my lifetime with the one chain; let alone rotating multiple.
I do have three chains for the Genesis after buying some at what seemed a good price at the time, however two remain waxed and unused; partially because I'm curious to see how long the original actually lasts.
Not sure I'd bother rotating a conventionally lubed chain (partially because of the mess) however I suppose it could serve as an appropriate point to give one a deep clean. That said I'd rather just wax everything... with multiple chains making it a bit easier to deal with the only downside of waxing - when a chain get wet and starts to squeak.
