Sensible is relative, look at the geography of Chile, the distances involved and the relations with their neighbors, then get back to me about sensible. In the time it would take to build the lines you would probably go through more than one bubble/downturn in the copper/lithium markets.
Building transmission lines is more than just having the copper available. You need the factories to build the cable, steel for the towers, right of way for the lines. All doable but not something that can be create quickly or easily and do you spin this up for a one time effort.
I love the development of solar energy but too many people forget all the logistics that go into transporting the solar from the best production areas to the consumer. Building the transmission lines from the desert, Atacama/Sahara/Mohave, to the consumers Santiago/Europe/Los Angeles ain't cheap, easy or fast.