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Wojowu
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What are the current views on consistency of Reinhardt cardinals without AC?

It's well known that Reinhardt cardinals are inconsistent, provided that we have access to axiom of choice, but, as far as I know, we are clueless about this when we don't assume choice. For me, the fact that Reihardt cardinals are inconsistent with choice already makes them, in a way, "wrong", that is, I'd believe personally that Reinhardt cardinals cannot exist in $V$ anyways. However, I have never seen any claims like this. So my question is:

Is it believed that Reinhardt cardinals can be consistent without choice? Are there any solid arguments for/against them? (other than "we haven't found them inconsistent, so they should be consistent")

Thanks in advance.

Note: I added soft-question tag because this question is more about philosophical views. Feel free to remove it if you think otherwise.

Wojowu
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