In (very) short: the resonance (notes interacting with one another), combined with the analog nature of varying velocity (how hard keys are pressed), combined with pedaling modifying both of the above.

The resulting combinatorial explosion means that the number of samples you need to capture, in order to have a high-fidelity reproduction of a physical piano, is enormous.

Putting aside the practicality of capturing all of this, you're still looking at tens to hundreds of gigabytes of raw samples per piano.

(Great question, by the way.)

Modeling also allows you to create an infinite number of instruments much more easily, and could allow someone to fine tune an instrument to just their liking