There have been a bunch in the last 10-15 years alone who have won Super Bowls or very nearly done so with good but not great QB's, and some who were just average.
The Giants twice with Eli, Ravens with Flacco, Denver with Peyton who was a shell of himself at that point, the Eagles with Foles and the Rams with Stafford.
You might even be able to throw Seattle with Wilson in there since he was a pure bus driver when they went to back to back SB's.
Then you have multiple teams who were a hair away from winning it in the Falcons with Ryan and the 49ers with Garoppolo, could even throw the Newton Panthers in there.
Obviously having an elite QB is the easiest way to win a SB but there have been plenty of teams just in the last decade or so who have won it all without one.