So, in the abstract an absolute reference frame eliminates paradoxes, sure, but isn't it the case that in the real universe, every version of the experiment in your blog that has been carried out has found no evidence of such a frame? Because if we're making claims about the real universe as Hossenfelder is doing, that means you can't actually lean on an absolute reference frame. The CMBR might kind of look like one if you squint, but the CMBR comes from matter that is in the end subject to the same relativity we are. Unless some version of the Mach principle turns out be real, with teeth.
It's really not. I have no idea from the video what the actual consequences of privileging the co-moving frame are on an attempt at creating a paradox except "maybe not a paradox! :)"