Density does directly scale with both of those in the form of more chips per die (=> lower cost) and smaller capacitance (=> less dynamic power dissipation).

If you want to reduce "effectiveness" of some process down to a single number, then density is far from the worst metric to pick.

Why is that all you care about? Stepping down a node gets you dramatically improved timing and design feasibility. The reduced density means you can pack the same design into less area. Your most challenging timing paths now have to traverse a shorter distance, and you can fit more of them relative to certain node-size invariant structures

isn't density a way to lower both the price and energy dissipation (so better heat management & energy efficiency)?