I don't think you can argue that it's mathematically equivalent. Just because space and time become so spread that they are effectively meaningless is not the same as them having not meaningfully existed and then existing. Neither can you really say that since any baryons that have not decayed are so far apart none of them interact that they behave like the concentration of all matter in the known universe. At those scales of time I'm not even sure that there are any left.

It's like arguing that one tiny piece of something in one place is the same as all the matter and all of space and time being in one place: it's I guess analogous but not equivalent. I will of course caveat and say that my undergrad physics degree did not cover end of the universe timelines lol. Kurzgesagt does have a video though.

The cyclical universe approach as I understand it is predicated on an eventual big crunch which I don't think is being argued anymore.