I am reminded of two things:

First, Szabo's "Money, Blockchains, and Social Scalability" where he makes the distinction between technological scalability and social scalability. Sure, fees go up when lots of people use a chain, but I think Shin is probably ignoring a similar pressure in centralized banking: regulators seem to tend to want to increase regulation which drives people toward the least regulated means of transacting. Shin's own BIS acknowledged this in a recent paper (#1450816). Szabo's paper is interesting to put into juxtaposition with Shin's:

When we can secure the most important functionality of a financial network by computer science rather than by the traditional accountants, regulators, investigators, police, and lawyers, we go from a system that is manual, local, and of inconsistent security to one that is automated, global, and much more secure. Cryptocurrencies, when implemented properly on public blockchains, can substitute an army of computers for a large number of traditional banking bureaucrats. “These block chain computers will allow us to put the most crucial parts of our online protocols on a far more reliable and secure footing, and make possible fiduciary interactions that we previously dared not do on a global network.”

When I designed bit gold I already knew consensus did not scale to large transaction throughputs securely, so I designed it with a two-tier architecture: (1) bit gold itself, the settlement layer, and (2) Chaumian digital cash, a peripheral payment network which would provide retail payments with high transactions-per-second performance and privacy (through Chaumian blinding), but would like Visa be a trusted third party and thus require a “human blockchain” of accountants, etc. to operate with integrity. The peripheral payment network can involve only small value transactions, thereby requiring much less of a human army to avoid the fate of Mt. Gox.

Second, Voskuil's "Utility Threshold Property" where he argues that

Higher fees imply higher hash rate cost mitigating the need to increase confirmation depth for higher value transfers. But given there is no way to reduce security for lower value transfers, the useful minimum value transfer rises with utility. Failure to support transfers in a certain value range implies substitutes are cheaper in that range. This implies the possibility of coexisting moneys to service distinct value ranges. However all Bitcoins inherently exhibit this property.

Shin says

fragmentation is not merely inconvenient — it is structurally incompatible with the network effects that give money its social value.

But I think that the fragmentation of liquidity that Shin finds so troubling also exists in traditional finance: I may be able to pay with Visa or Mastercard, but those are effectively separate systems. The only reason they work well together is that we have decades of building infrastructure around them.