You are hitting at the core of the issue. If you do the math with how people use bitcoin today, you’ll get one answer; but if you do the math with how people could use bitcoin today, you’ll get maybe 1.5-2.2x that answer (eg, many users creating multi-input multi-output transaction with only one aggregated schnorr signature hitting the chain). In an ideal world though, this gets maybe 1M transactions per day max. 

If you look at L2’s, you’ll get maybe 100-1000x the answer above (random guess, tbh)…but a lot depends on how people use those L2’s. If you look at how I’ve tried lighting, it’s like only a 2x improvement…because keeping a lightning node running isn’t trivially easy. And one can argue this isn’t truly sovereign, just more sovereign than status quo money. And getting to this hypothetical 100-1000x requires time…the 1000x will require 10x longer than the 100x improvement. One could argue the improvement is unbounded, but imho, lightning channels and liquid peg-ins won’t have infinite lifespans. 

Then there is a weird category of utxo sharing where the transaction signature somehow communicates what percentage of the utxo is available to the user. I can’t ballpark the efficiency gain here, it might be no improvement on a per spending transaction basis…but could be really big improvement in terms of allowing one output to be owned by 10 or maybe 100 people. 

But AFAICT, we are far far away from letting 1B people use the chain once a day. 

 This is how I’m imagine it:

We’ll have many interoperable ecash federations using Lightning to clear bitcoin between each other. 

Federated ecash would be perfect for everyday transactions. Anonymous, very small transaction fees. 

I’m not aware of any reason why this model cannot scale to billions of transactions per day. 

The federations would be geographically distributed with trusted but anonymous federation managers so they’re difficult for governments to attack and suppress. 

 I agree. Federations could federate over bitcoin itself but also lightning channels or liquid peg in transactions…each of these offers different self sovereignty trade offs, but all are massively better than the status quo.