It's a two fold issue. First, NHTSA,and others, have increased the safety regulations, that forced the weight up. Second, 'adding lightness' is expensive.
When I was working for Mosler, we built a 900kg (1984lbs) car, powered by an LSx. Before the side airbags were required, but it did have front air bags, and minimal interior amenities. It also had a full carbon tub, bare carbon interior, etc. It can be done, but it's expensive, and even more expensive and difficult with today's standards.
https://www.motortrend.com/news/2002...-mt900-photon/