I think we can understand Jain's comments as follows: when you look at the $n=1$ Landau level fully filled wavefunction $\psi(z_1,z_2,...,z_N)$as a function of one particle, say $z_1$, it has $N-1$ zeros. All of them are exactly at other particle positions. So it does not have any wasted zeros. In other words, if one additional particle, say $z_{N+1}$, is added to the system, and you necessarily need to create at least one more additional zero in the original wavefunction to ensure the Pauli exclusive principle between $z_1$ and $z_{N+1}$. However from the one particle quantum mechanics, we know that in general, adding one more node to the wavefunction requires finite additional kinetic energy. In other words, to change the density of particle by infinitesimal amount, $1/N$ here, you need to input finite amount of energy. This, by definition, simply tells you it is incompressible.
Incompressibility simply means the spectrum is gapped, as pointed out in these discussions Incompressible quantum liquid. And I think having the wavefunction itself does not tell us whether it is compressible or incompressible since the spectrum depends on the Hamiltonian. In the current case, the Hamiltonian contains only kinetic energy. Therefore the above arguments applies. If the Hamiltonian also contains interaction term, the arguments in the previous paragraph do not necessarily lead to a finite spectrum gap.
