  We demonstrate that the plasma analogy is generally unreliable at predicting
the edge properties of quantum Hall (QH) states, as it fails to account for the
local edge velocity. This discrepancy arises from a fundamental difference
between QH droplets and Coulomb gases (CGs): the former are incompressible
liquids subject to area-preserving deformations, while the latter are governed
by electrostatics and thus involve conformal transformations. We illustrate
this QH/CG mismatch across various examples and show its impact on physical
quantities, measurable in both solid-state samples and quantum simulators.
Specifically, we discuss fluctuations of local observables and their connection
to state-of-the-art microwave absorption experiments.
