@redshiftdrift @jimdonegan
I think there is something highly intriguing not cited in that paper: https://iopscience.iop.org/article/10.1088/0264-9381/4/6/025
if we agree that the universe is more complex than the Friedmann class can provide, the fits of such a cosmology will reveal shortcomings at some point. If this point has arrived now, synchronising all probes (e.g. by BAOs) across all scales an time, we will still end up with tensions, see here for more details: https://arxiv.org/abs/2203.11219