Require vast investments to add the capacity to handle storage and would be less efficient.

Your proposal is basically to spend 20% to 30% more money, loses and extra 4-7% electricity every charge discharge cycle and gains effectively nothing which is why nobody is doing it.

> how you top up local storage during supply peaks when you haven't got a local surplus.

Peak + filling storage requires extra transmission capacity which costs money to build and energy to use.

> At the end of a different transmission line.

Transmission lines work in either direction and are generally set up as an interconnected mesh. You want redundancy from the solar power plant to customers, but you also want redundancy from batteries to customers.