I see where I missed your point now, thanks for your patient explanation-
I thought you meant 'market-cap' to be the value of the items lodged in the
blockchain/notebook.

You mean it as the sum of the value of the tokens.
The act of writing to the notebook is an (increasingly?) non-free competition
with tokens as reward.
The ability to write to the notebook is protected by 2 components:
1) The value of the bitcoins/tokens
2) crypto-difficulty

If the reward/token 'value' diminishes to a point <= cost of
participating in the competition...what happens?
Collapse or the value of the tokens must increase.
Or something we have not thought of.
Perhaps fewer will still compete.
But devaluation is addressed in the protocol by scarcity,
we just do not yet know if that will work as we only have 1 datapoint
re: blockreward reductions. But the datapoint is a nice one thus far,
there has been an explosion of mining even after the block reward
halved.

So if we try to answer OP's question:
Such a technology's existence and continuation would have to leverage
some force equal-to or greater-than human self-interest.

Existence and persistence of the ledger is woven to the valuation
and is not seperable ( without collapse ).
The value of the token gives rise to the ledger, is intrinsic to the scheme.
So token value, which I'm seeing as fundamental, has to be replaced by *something*.

That something will have to be human-nature proof to overcome
governments and wealthy theives/cheaters.
What is stronger than their collective might?
Self-interest, which is fundamentally human.

VC money is more interested in the blockchain, certainly,
but they already have wealth.
They appear to be pouring money into investigating how to
build this thing out.

Bitcoin just aligned the aims of Ukraine and Russia-
they both decided they need to squash it.