Black holes embedded in FLRW cosmologies

There has recently been some considerable interest expressed in a highly speculative model of black hole evolution – allegedly by a postulated direct coupling between black holes and cosmological expansion independently of accretion or mergers. We wish to make several cautionary comments in this regard – at least three exact solutions corresponding to black holes embedded in a FLRW background are known, (Kottler, McVittie, Kerr-de Sitter), and they show no hint of this claimed effect – thereby implying that this claimed effect (if it exists at all) is certainly nowhere near ubiquitous.