Favre and Brees and Brady were drafted in completely different time frames than today. Carr is in a similar situation as Mariota so I don't think he is a great example. And the Bengals haven't won a playoff game with Dalton as the starter and he has been pretty average most of his career. It is certainly possible to find guys in later rounds, but if you look at more recent history, almost every top tier QB was a first round pick, with the exception of Russell Wilson. Of the current starting QBs in the league (not including back ups playing for injured QBs) only Brees, Brady, Wilson, Dalton, Carr, Foles, Garoppolo, and Cousins were drafted outside the first round. 2 of those were drafted almost 20 years ago, and other than Wilson, the rest are pretty average.
ETA: I accidently left off Dak, who has been a solid QB who wasn't drafted in the first. I didn't count Keenum, Brissett, or Fitzpatrick since they are really just back ups acting as place holders for the time being.