But it say it’s functional for only up to 5 hours after dead battery so there is a power component to it. As in, it’s not completely passive like other passive NFC.
Well no you're also incorrect, according to TfL the daily cap for zone 1-6 which 99% of journeys are in is £12.80 and at worst if you travel to zone 9 then its £18.30.
Bear in mind that the maximum you can spend on your Oyster card in a day is, I think, around £10. So in the worst case that's the most you could lose - nobody would be able to use it in a shop to pay for anything.
I think the compromise is fine and certainly no worse than losing your actual oyster card or contactless credit card
And i recall that you can register your Oyster Card online so if it’s lost or stolen you can turn it off and move the money to a new one. Which presumably you’d do if you are a constant transit user.
And I’d be more worried that you lost your phone cause those are way more expensive to replace
Because OFF means OFF. Let's get OFF done! When the phone turns itself off due to low battery, it's not fully off. It's in that "you can still take the tube and I've enough power to keep the NFC chip active" mode.