Personal note re the "roast / roost" question: I'm in my seventies -- from earliest years, had been aware of the expression "rule the roost": it was only decades on, that I came across the "rule the roast" version -- if I recall rightly, in Regency-setting fiction (Georgette Heyer, maybe?). I was so used to the other version, that the "roast" one (although it makes sense) felt goofy and strange to me, and still does. I see "ruling the roost" as making good sense -- in that the "rooster" synonym for cockerel, has (genuinely, I believe) connotations of a diligent and conscientious one -- in so far as birds can be such things -- who will, as well as copulating with his hens, look after them; including that they're safely tucked in to roost overnight.
Have often seen this modification explained as: the great majority of people nowadays, are oblivious to any sort of lore about riding or driving horses; but are more au fait with monarchy-related stuff -- "free rein" means nothing to them, so they parlay it into "free reign": which is basically sense-making, though with -- as catseye says -- implications of large-scale domination / control, rather than just one's horse(s) controlling the journey.