I disagree. Or rather I think you describe the near future, but not the (slightly) more distant one.
We will realize there are two decomposable activities here:
-1- Ensuring time is single threaded and permanent.
-2- Tracking the contents of the block chain.
Right now these are fused. But once they are separated then there will be a single master chain, whose sole purpose is to house the Merkle roots for all of the specialty chains.
This master chain probably itself is sharded just to provide lesser guarantees of single threadedness, but at a much higher number of times per minute.
Now all of the specialty chains can be much more light weight since they are not carrying the burden of ensuring non-reversibility, they just publish their merkel root to the main chain regularly for this purpose. Instead they must relably store and provide access to the historical content of their independent chain.
Why do I think this?
Because the act of ensuring non-reversibility **IS** a network-effect type of operation. The more resources/entites supporting the non-reversibilty of a chain, the more robust its non-reversibilty guarantee becomes. (just as with a network the more in the network the stronger it becomes.) Second the burden of supporting each new participant in the system does not grow as the number of supported participants grow.
In this case, the logical conclusion is pool all resources into a single chain. But it wont be a chain optimized as they are today, for end-user transactions. Instead it will be adapted for maximum security, moderately fast block rate, and low data volume.
But then under that single chain, many chains will live. (Note these are not really L2 chains, as we presently understand that term, since they never settle back into the L1 chain.)
Anyway, that is my take.