Has the ${cal N}=1$ Minimal SUSY standard model been ruled out by the nature?

Question: Has the ${cal N}=1$ Minimal SUSY standard model (MSSM) been ruled out by the nature? What are the natural constraints that ruled out such ${cal N}=1$ MSSM?

In particular, the ${cal N}=1$ MSSM, such as the theory mentioned in Ramond’s book "journey beyond the standard model" includes two Higgs (to cancel the $SU(2)$ Witten anomaly) to write down the Yukawa interaction superpotential.

From what I read from the book, here are possible natural constraints to rule out ${cal N}=1$ MSSM:

1. We already discovered a single Higgs standard model, we do not have two Higgs (and their Higgsino) discovered yet. So does the two Higgs ${cal N}=1$ MSSM problematic?

2. (from Ramond’s p.289): The theory is invariant under unphysical symmetry (What exactly? Can someone clarify this?)

3. (from Ramond’s p.289): The theory has unphysical ground states (What exactly? Can someone clarify this?)

For those who are not familiar with these statements, here are the relevant paragraphs from Ramond’s book for convenience:

The Yukawa interactions of the MSSM are the same as in the $N = 0$ standard model, but of course written in a manifestly supersymmetric-invariant form. Hence they appear in the superpotential
$$
W_{MSSM}=mathbf{Y}_{ij}^uPhi_mathbf Q^iPhi^j_bar uPhi_{H_u}+mathbf{Y}_{ij}^dPhi_mathbf Q^iPhi^j_bar dPhi_{H_d}+mathbf{Y}_{ij}^ellPhi_L^iPhi^j_bar ePhi_{H_d}tag{10.3}
$$
where $i,j = 1,2,3$ are the family indices of the three chiral families.

This superpotential reproduces the Yukawa couplings of the standard
model, but with one important difference. We recall that the one Higgs
field of the standard model does double duty, coupling to charge $2/3$ quarks, and its conjugate to charge $-1/3$, $-1$ quarks and leptons, and giving all fermions their masses. Supersymmetry does not allow conjugates to appear in the superpotential which has to be holomorphic in the superfields. As a result, hypercharge conservation forbids the same Higgs superfield from coupling analytically to both sectors. With only one Higgs field, some quarks and/or leptons would stay massless.

Unfortunately, this simple cubic superpotential cannot by itself re-
produce the real world for two different reasons: it is invariant under
unphysical global symmetries, and it generates a potential which does
not have a physically-acceptable ground state.