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 independent 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 Friedmann-Lema\^tre-Robertson-Walker 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.