So to the point...how does a capped financial system, which at some point will only be able to diminish in total quantity (and will do so continuously) manage to escape eventual extinction (regardless of divisibility), or at the very least dramatically reduced availability to the point of compromising the very economies it creates...?
Regardless of divisibility?
What do you mean by "regardless of divisibility"?
Divisibility is exactly the reason that this isn't a concern.
As bitcoins are lost, the available supply is reduced. Economic effects result in the remaining bitcoins being worth more. This means that instead of spending 10 mBTC for a sandwich, you are eventually spending 10 µBTC (see how divisibility makes that possible?). As a result, the remaining bitcoins are spread thinner. This means that each individual with the same wealth has less bitcoins than they would have had in the past.
If any of these individuals lose their bitcoins, the supply is diminished, and the value of the remaining bitcoins increases. Eventually (a few centuries from now) instead of spending 10 µBTC for a sandwich, you'll be spending 10 nBTC. As a result, the remaining bitcoins are spread thinner. This means that each individual with the same wealth has less bitcoins than they would have had in the past.
If any of these individuals lose their bitcoins, the supply is diminished, and the value of the remaining bitcoins increases. Eventually (a few millennia from now) instead of spending 10 nBTC for a sandwich, you'll be spending 10 pBTC. As a result, the remaining bitcoins are spread thinner. This means that each individual with the same wealth has less bitcoins than they would have had in the past.
And so on, and so on.
Eventually there is only 1 pBTC (0.000000000001 BTC) remaining in existence. But because of divisibility, it is broken into 1,000,000,000,000 yBTC pieces spread throughout the economy.
This process can repeat as many times as you like.