[...] in the event of a private key collision, where two different users independently generate the same private key and sign messages with it in the same block, wouldn’t that create a conflict? It seems like a situation analogous to a "double spend" or a "double reserve" of the same key. Both parties could claim ownership at the same time in the same block.
Thanks for giving some insights about your use case. I had previously written another answer (about inheritance and similar constructs) but I think this no longer applies after your answer.
There's however imo a misunderstanding on your part. If "private key collisions" were a problem for Bitcoin, then Bitcoin would be completely broken. Thus, your "proof of ownership" approach is not necessary.