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-Lemaître-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.