Those are all somewhat larger ICL cameras, not compacts
Here's an example of a compact. See page 7.
Electronics forum for electronics experts to repair defective appliance.
elektrotanya.com
Ken Croft has been on this forum long enough for me to believe him if he says he has stripped 2 of these cameras and not seen a button battery.
Ken said he hasn't found the battery, but he also hasn't said he found a capacitor, and he has only ever posted to this forum photos of one side of the main circuit board. So, completely inconclusive.
Your reference to the Olympus which has a thread about a battery in the motherboard is also an ICL camera, and the lone thread for Olympus that refers to that kind of battery in that brand. All that said, If anyone wants to disassemble or look at the motherboard of a dead Olympus Stylus 1/1s and take a picture - I will accept that as the final answer.
I've disassembled three, and they have a battery. I changed it in one of them. If I get another one for repair, I'll take pictures to put this myth to rest, at least for this specific camera. But will the myth then persist for other cameras?
For practical purposes most compacts wouldn't need days of clock battery function because the main battery can be charged in the camera (the stylus 1/1s can't). I imagine there's the case of people without extra batteries or don't carry extras. But the camera is plugged in the same day typically. Which is why a capacitor might suffice, if that helps explain where the "myth" as others call it or perhaps "truth" came from.
Imagine you're engineering a camera: you know that some people, some of the time, will plug their camera into USB. It could be 10% of users, it could be 75%. But you also know that 100% of all people will always, every single time, have to put a lithium-ion main battery into the camera in order to use it, so what do you design the camera to use? The 10-75% possibility of charging the clock's power supply,, or the 100% guaranteed possibility of charging the clock's power supply?
I suspect the myth came about because many people are unaware that button cell lithium batteries are rechargeable. Some cameras use non-rechargeable and user-replaceable coin cell lithium batteries, so I think the idea of small lithium batteries being rechargeable seems odd to a lot of people, therefore they started guessing it was a capacitor and then stating their guess as fact. (If you google the model number of the button cell battery, however, you will find charging specifications.)
And now, the latest test result: in which I matched the settings precisely between my two Stylus 1s (one that maintains time for an hour+ without the main battery; the second which does it for 10 minutes), and allowed them to sit overnight with a freshly charged main battery. Does the second one now maintain time for an hour+? Nope. Now I'm plumb out of theories, so I'll end with this:
Your experiment that it takes hours to charge, not seconds or minutes, proves that it's a battery. You literally already proved it for yourself and everyone else - you're just so stuck on confirmation bias for your initial theory that you're misinterpreting your own results.
In any case - as to the OP's question: should he return the camera based on this function? I say no. Rather, I recommend buy some aftermarket extra batteries and a multi-battery charger. It takes less than a minute to change batteries and hopefully that is enough so your camera doesn't lose time. Even if it isn't, resetting time every battery exchange wouldn't bother me. Especially with the very long battery life of it's battery.
I agree. If you lost settings in addition to the clock resetting, that would be more of a hassle, but settings being lost is a thing that cameras haven't had to deal with in decades, since they switched from storing settings in volatile RAM in the late nineties and very early 2000s to non--volatile flash memory. However... it's another myth that persists, as we have seen in this very thread.
You'll also see a lot of times on this forum that people will suggest leaving the main battery out overnight or 24 hours or a week as a way to troubleshoot a camera that has a problem, saying that will reset everything. It will work for a 20-year-old camera, but not a modern one, yet a misunderstanding of how cameras are made now allow that bad advice to persist.