The Steady State hypothesis isn't really a class of hypotheses, it was a specific one. The Steady State hypothesis predates the entire concept of metric expansion, after all.
History, everyone. Olber's paradox is important because of the history, not its relevance to 21st century physics.
The model I described is the historical model, as developed (and later repudiated) by Einstein. It does not "predate the entire concept of metric expansion". The whole point was to reconcile expansion, which was both predicted by GR and confirmed by Hubble's observation of recessional redshift, with the belief that the Universe was infinitely old and unchanging.
And there were many variants of Steady State, as the model was discovered independently after Einstein, and refined throughout the 1950s as its adherents struggled to explain new observations that distant quasars are far more common than near ones. There was even a brief (and apparently failed) attempt by Hoyle to revive a Steady State as late as 1993, involving widely varying rates of expansion in different regions of the Universe.
What ultimately disproved Steady State was seeing the CMBR. None of this has anything to do with Olber's paradox, which is not an issue in a Steady State model for exactly the same reasons it's not an issue in modern cosmology.
History, everyone. Olber's paradox is important because of the history, not its relevance to 21st century physics.