Beane did his job that draft for sure, but I am 100% sure McD picked Allen. Allen and Darnold are "process" guys, team-oriented hard workers who focus on football perfection. Mayfield and Rosen did not have that reputation. Mayfield was known for partying and Rosen for dissing other players. Although Mayfield and Darnold were predictably gone, there was shock - shock I tell you - when the Bills picked Allen over Rosen. All the analytics guys had Rosen by a mile, all the pundits had Rosen by a mile, TBD had Rosen by a mile. Beane worked his way to get Allen because McD wanted him, against all conventional wisdom to the contrary, and that was genius.
The Mahomes miss has been subject of numerous threads, suffice to say the Bills were not the only team to miss on him, including the Bears who needed a franchise QB and chose Trubisky. We didnt need a QB because, you know, we had EJ Manual coming into his own, just ask then-GM Doug Whaley.