If that is true, then the units might not be rare but blockchain space might indeed be very scarce (and then must be somewhat expensive). It is a useful perspective.
At 8 billion people and 1024 account balances each, and say 128 bytes per account storage, that is 1 Petabyte. That is the best the mini blockchain could do. One-time ring signatures would make it entirely intractable (100s or more of Petabytes) unless you increase the cost until the 8 billion are restricted.
Let's assume a 10 year goal of 1 billion x 8 account balances each, so 1 Terabyte which is one hard drive. And hard drive space doubles every 18 months, so in 17 years we can store 1 Petabyte on one hard drive. So the mini blockchain can scale.
So there is no scarcity, except
for badchosen design (priorities).
P.S. we do have to discourage dust balances though.