Yes of course having a great QB, the face of the franchise, a single entity that the team is recognized by and a player that literally Carries the team on his back to victory is what every fan dreams of. And yes QB is the most important position On the team.
That doesn't mean you have to have a "franchise" QB to win. Unless your definition of "franchise" includes names like Flaco, Wilson or Kapernick and many more that I have highlighted in the list below.
A great defense, solid running game and a QB who doesn't make mistakes at critical times in the game is just as good recipe. Of course having a franchise QB is the most attractive way of doing it. The problem is they only come around every so often. They are rare. Some teams spend decades looking for one. Some have gotten lucky but most just suffer through years and years of mediocrity by reaching for QBs higher than they should out of desperation to have that figure head.
Super Bowl 1. Bart Starr (MVP), 2 TDs
Super Bowl 2. Bart Starr (MVP), 1 TD
Super Bowl 3. Joe Namath (MVP), 0 TDs
Super Bowl 4. Len Dawson (MVP), 1 TD
Super Bowl 5. John Unitas (Chuck Howley), 1 TD
Super Bowl 6. Roger Staubach (MVP), 2 TDs
Super Bowl 7. Bob Griese (Jake Scott), 1 TD
Super Bowl 8. Bob Griese (Larry Csonka), 0 TDs
Super Bowl 9. Terry Bradshaw (Franco Harris), 1 TD
Super Bowl 10. Terry Bradshaw (Lynn Swann), 2 TDs
Super Bowl 11. Ken Stabler (Fred Biletnikoff), 1 TD
Super Bowl 12. Roger Staubach (Harvey Martin & Randy White), 0 TDs
Super Bowl 13. Terry Bradshaw (MVP), 4 TDs
Super Bowl 14. Terry Bradshaw (MVP), 2 TDs
Super Bowl 15. Jim Plunkett (MVP), 3 TDs
Super Bowl 16. Joe Montana (MVP), 1 TD
Super Bowl 17. Joe Theismann (John Riggins), 2 TDs,
Super Bowl 18. Jim Plunkett (Marcus Allen), 1 TD
Super Bowl 19. Joe Montana (MVP), 3 TDs
Super Bowl 20. Jim McMahon (Richard Dent), 0 TDs
Super Bowl 21. Phil Simms (MVP), 3 TDs
Super Bowl 22. Doug Williams (MVP), 4 TDs
Super Bowl 23. Joe Montana (Jerry Rice), 2 TDs
Super Bowl 24. Joe Montana (MVP), 5 TDs
Super Bowl 25. Jeff Hostetler (Ottis Anderson), 1 TD
Super Bowl 26. Mark Rypien (MVP), 2 TDs
Super Bowl 27. Troy Aikman (MVP), 4 TDs
Super Bowl 28. Troy Aikman (Emmitt Smith), O TDs
Super Bowl 29. Steve Young (MVP), 6 TDs
Super Bowl 30. Troy Aikman (Larry Brown), 1 TD
Super Bowl 31. Brett Favre (Desmond Howard), 2 TDs
Super Bowl 32. John Elway (Terrell Davis), 0 TDs
Super Bowl 33. John Elway (MVP), 1 TD
Super Bowl 34. Kurt Warner (MVP), 2 TDs
Super Bowl 35. Trent Dilfer (Ray Lewis), 1 TD
Super Bowl 36. Tom Brady (MVP), 1 TD
Super Bowl 37. Brad Johnson (Dexter Jackson), 2 TDs
Super Bowl 38. Tom Brady (MVP), 3 TDs
Super Bowl 39. Tom Brady (Deion Branch), 2 TDs
Super Bowl 40. Ben Roethlisberger (Hines Ward), 0 TDs
Super Bowl 41. Peyton Manning (MVP), 1 TD
Super Bowl 42. Eli Manning (MVP), 2 TDs
Super Bowl 43: Ben Roethlisberger (Santonio Holmes), 1 TD
Super Bowl 44: Drew Brees (MVP), 2 TDs
Super Bowl 45: Aaron Rogers (MVP), 3TDs
Super Bowl 46: Eli Manning (MVP), 1 TD
Super Bowl 47: Joe Flacco (MVP), 3TDs
Super Bowl 48: Russell Wilson, 2TDs
() denotes who the MVP of that game was, if it says MVP, the Super Bowl winning quarterback won the honor. After the MVP is the total touchdown passes each winning quarterback threw in the game. This does not include any rushing touchdowns a player may have had. Steve Young has the record with six touchdown passes in Super Bowl 29.
I don't know where the all highlighted guys were drafted but I know none of them were elite. Most had really good defenses and really good running games to lean on.