Thanks to @ace and to everyone who has contributed to this discussion.
Quick summary: If you have devices registered to AND logged into the same Apple Account, AND if you want AppleCare+ with Loss and Theft for them, AND if the total cost of separate AppleCare+ policies is more than AppleCare One (be sure to compare monthly totals and annual plans), then AppleCare One is worth considering.
Longer story:
I just had my first — and likely last — experience with AppleCare One and it was dreadful, resulting in five days of phone calls with six different people at AppleCare Support, and me losing the AppleCare+ (without Loss and Theft) coverage I had for my wife’s iPhone and ending paying more for AppleCare+ with Loss and Theft for her phone, outside of AppleCare One.
The first-round AppleCare+ on my iPhone expired and I was happy to renew, first annually. The AppleCare process on my phone pushed me to AppleCare One, and pushed even harder, over and over, to add my wife’s phone. It was cheaper to do so, so I did.
Then, three times a day for five days, I received vaguely threatening e-mails telling me I must change the Apple Account login on my wife’s phone, and her phone’s AppleCare was marked as “pending for 24 hours” for five days. She uses a different Apple Account than I do, although her phone is registered under my Apple Account (probably a remnant of when we shared our Apple Account ages ago).
I’ll spare you the ugly details of the often-contradictory, often-nonsensical interactions with AppleCare support, and just offer the warnings and suggestion:
• If you have AppleCare+ without Loss and Theft coverage, and if you give it up by joining AppleCare One or anything else, you can’t get it back, ever. It’s no longer offered by Apple, so even if Apple sells you AppleCare One you can’t use, and you try to undo it, you won’t be able to go back to the simpler version of AppleCare and will be forced to go to the only version now offered, with one with Theft and Loss.
• All of your devices under AppleCare One must be registered AND LOGGED INTO the same account. This is most definitely not a Family program.
• Unlike other Apple Support teams, who in my long experience range from good to amazingly excellent, the AppleCare team is inflexible about fixing what is clearly a mistake in the AppleCare One onboarding process, so don’t expect useful support. You know things are bad when they ask if you read the fine print (I replied that I only read the BIG PRINT on my small screen, which over and over boldly told me that I should add her phone to the plan, and even now is touting AppleCare One overall) and claim inflation is the reason for the price difference (it can’t be because we were on a monthly plan for her phone, so it was “current”), among other stalling tactics hoping I’d just hang up, pay the difference and go away.
I just had the battery in my phone replaced under AppleCare last week, and hers is due soon, so we are pretty happy having AppleCare for the time being. We don’t buy phones very often, so we re-upped for a year of each (slighly discounted from a monthly subscription). As I told her today at the end of all the unpleasantness with AppleCare support, “I don’t deeply mind the result — financially we ended up being out about $16, which I’ll swallow reluctantly. It was the process that hurt.”
Overall — if you have devices both registered to AND logged into the same Apple Account, AND if you want AppleCare+ with Loss and Theft for them, AND if the total cost of separate AppleCare+ policies is more than AppleCare One (be sure to compare monthly totals and annual plans), then AppleCare One is worth considering.
If ANY of those are not true, then beware. (Even if they are true, beware.). Apple is definitely not flexible on this and is showing no intent to accommodate and fix even its own mistakes.