In the first round the referees have pointed out that it is well known that mean field approaches are not expected to properly describe correlations (also dynamically) and in particular higher momenta of observables. Therefore in general the symmetries of the microscopic Hamiltonian are not satisfied.
Although the authors have not appreciated it, both referees mentioned that the failure of the GPE of properly describing the evolution of <L_z> would have been very surprisingly. Not, however, the failure in describing higher momenta of L_z or any other operator.
In the new version the authors instead of amending the original claim, put all the emphasis - also in the reply to the referee's reports - on explaining that many body theory is needed to preserve/recover the symmetries of the microscopic Hamiltonian.
In this respect let me also notice a small logical loophole in the reply of the authors.
As the author mention it is well known (appendix A is rather useless indeed) that conservation laws related to a generator A implies the d/dt<A^n>=0 for any n. If the latter is not satisfied the global symmetry is not preserved by the approximation used. The author in particular use the fact that for n=2 GP shows some evolution and they claim this effect being surprising and therefore the need to go beyond it.
On the other hand they also write in the reply that:
" [..] it is very well known that fluctuations are not accurately described by the GP mean-field or any other mean-field. However, fluctuations as such are not the topic of this work."
Now fluctuations correspond to the case n=2 and therefore it is also not surprising that GP is not symmetry conserving.
As for the previous round I cannot recommend the publication of the manuscript in its present form,
since the authors' aim is to convey the massage that they have discover that GP mean-field equations do not properly describe higher momenta of observables (and therefore for the observables generators of a symmetry of the Hamiltonian, GP does not preserve the symmetry of it). What it is interesting is to quantify the failure of GP for some quantities and how "hard" is to cure it.
Concerning the (added) results:
1. The results on <P^2> and the emphasis (in the reply) put by the authors on the deviation of the GP result even when the depletion is negligible, is almost not new.
It has being discuss in the context of uncertainty in ref , where the authors offer also an explanation of why the large deviation in the time evolution occurs within a GP approach.
2. Sec 2.5 should be an Appendix if they want to keep it.
3. Appendix A is textbook.
As a final comment let me stress that I do recognize clear merits of the manuscript: it is well written (forgetting the parts concerning their major claim) and with a pedagogical aim; they use some quite general examples to quantify, at least to some extent, the failure of the GP in describing the evolution of n=2 (and n=3) momenta and show how including more orbitals the situation is improved.
I find their results together with the ones of Ref  and of the not-cited paper by Klaiman and Cederbaum [PHYSICAL REVIEW A
94, 063648 (2016)] (which in my opinion has to be cited) useful to get a better understanding on the GP mean-field equations.