Hello and thank you.
The trouble is that the security of a public blockchain is proportional to the amount of full nodes that run it — as you could see in the recent 51% Ethereum hack, even large chains are susceptible to this type of attack. So reducing the amount of full nodes on a chain will also make it less safe, whereas increasing the amount of nodes on a chain will necessarily make transactions more expensive.
At the same time, it will not, actually, save the nodes from the scaling problem, because every added client contributes to the load on every node.
There is no way to scale a “typical” chain without some type of segmentation, but segmentation will necessarily reduce the security of every segment by reducing the available hashing power.
In the light of current events and past experiences, I simply don’t see how “publicly writable” systems can be made feasible, scalable and safe enough to handle money. I think it would be easier and cheaper for everyone to have some sort of federated solution with secured “islands” and public API access.