Ishtar is certainly free to conclude that mortals can gain hakai, but her conclusion is based on shaky evidence. We do not know enough about Genesis to understand if she even is still mortal, and she is the only example.
If we see Rex outright annihilating stuff the way a God of Destruction can, he'll be a real problem. The stars aligning for one creature with a particular powerset to gain diet hakai isn't really worth being on the gods' radar right now.
At best, this is like concluding Alcatraz is insecure because one inmate broke out of it. And that's with concluding ambiguities in favor of the 'insecurity of hakai' argument.
If you (and Ishtar) think killing people makes choices for them or erases the choices they make, I'd like to see the logic leading up to that. If I control your mind, then I am taking away the ability for you to choose. If I travel back in time and manipulate events to achieve a different outcome, I am destroying the choices you already made and wearing away at your ability to choose each time I replay a particular moment in time to try to make people choose differently. If you decide to live and I kill you, I haven't made your choice for you. You made your choice, then simply failed to actualize it.
Ishtar's initial charge was hypocrisy. Security of hakai does nothing to prove Asha'rah violated her own worldview, since she intended to make hakai secure. The security of hakai is therefore irrelevant, not supplementary.
Asha'rah ruined many things with her rebellion. Striving is not one of them. Nobody's choices were erased. Nobody started having their choices made for them.
If Ishtar doesn't care for Asha'rahs's perceptions on "the reasons for mortal life, or why/how Gods find meaning in mortal striving," then she will never be able to make her point of Asha'rah being a hypocrite. Hypocrisy is not about the merits of any particular values system. Hypocrisy is about a person violating their own values system. Asha'rah gave Ishtar the context she would need to make a proper judgment about hypocrisy - i.e. Asha'rah's own values system.
If Ishtar thinks Asha'rah messed up, is a lousy god, is a liar, or is failing to treat hakai the same way as time travel when she should, these are all things which can be discussed on their own merits. But none of them have anything to do with hypocrisy. To show Asha'rah is a hypocrite, Ishtar needs to show that Asha'rah is failing to follow her own values system, not that Asha'rahs' values system is flawed.
Correction to my own earlier assertion: Parsley also says that Asha'rah is a hypocrite, due to what you quoted. My bad on missing that. I'll quote it again so it isn't lost: "The fact is you wield a power you have no right to possess, just as this alternate Jinzi Pantaloons also wields a power he has no right to possess. That you saw fit to declare that the gods of old should have placed tighter restrictions on time itself to prevent the latter, while acknowledging the former, makes you a hypocrite."
Parsley's statement is based on an underlying assumption that hypocrisy can be applied from failing to follow an external code, namely Asha'rah violating the laws of Heaven. This is seen in her talk about rights of possession. But hypocrisy is about violating one's own code, not the code of somebody else. In the first place, the reason why Asha'rah tried to make Hakai secure at the time of its conception and the reason Asha'rah wants time to be secure are very different reasons.
Hakai can cause a lot of destruction and is meant to be a clean up tool of the gods, so making it secure was good sense, but Asha'rah has no inherent philosophical objection to mortals ever using hakai. The fact that mortals can be promoted to godhood shows that they can be deemed trustworthy enough to be granted hakai, just as they might be deemed trustworthy enough to be elevated to Kami (the vetting process for all this is obviously flawed, hence people like Hammer). Asha'rah has no inherent problem with mortals eventually gaining hakai or beings other than Gods of Destruction trying to gain hakai, at least beyond her overall objection about the exponential power of martial might which was the cause of her rebellion.
Asha'rah's problems are with time manipulation, for the reasons stated above. If Asha'rah had groused about how they should have made hakai completely secure and out of reach of anybody (i.e. never created hakai in the first place), then Asha'rah would be a hypocrite since she herself stole hakai and regret it. But since Asha'rah groused about time manipulation, then Parsley would have to show that stealing time isn't against Asha'rah's own code to prove Asha'rah a hypocrite. Comparing it to Asha'rah stealing hakai doesn't work because Asha'rah's own values system treats the two powers differently.
So equating time travel and hakai as things which "can do incalculable damage in the wrong hands" has objective merit as a comparison, but holds little value in this argument because Asha'rah's views on why hakai should be secure and her opposition to the use of time travel are based on different reasons, and she only has direct philosophical objections to the latter.