Not sure why Weeb shouldn't be in the conversation

He was a pretty average coach by any measure.
But I voted Switzer -- even though he's FAR from a bad coach. Dude won big in pros and college, can't front on that toooooooooooo much.
Ewbank's certainly not an average coach by the one measure highlighted in the OP, which is number of championships. And he built two teams from the ground up. He was responsible for getting Unitas and Namath on those teams.In 1946, the All-America Football Conference (AAFC) was formed. That's where the Cleveland Browns and San Francisco 49ers were formed. One of the founding teams was the Miami Seahawks, who sported
this hot logo. They still finished with the worst record in the AAFC, and relocated to Baltimore and named themselves the Colts (rich horse racing/breeding tradition in Baltimore, obviously). The Colts went 2-11-1 in 1947, 7-7 in 1948 and then 1-11 in 1949. Due to the politics involved, when the NFL merged with/swallowed the AAFC, they took the 49ers, Browns ... and Colts. The Colts were awful in the AAFC, and in 1950, predictably finished 1-11 in the NFL.
After that, the team (
donning green and silver) folded.
In 1951, a team called the New York Yanks (with their own dubious, complicated franchise history) went 1-9-2 that season and sold themselves back to the NFL. They were repurchased by Giles Miller and moved to Dallas, and played the '52 season as the Dallas Texans. That team went 1-11, and did so in particularly ugly fashion. Miller sold the team back to the NFL, and a few months later they were sold to Carroll Rosenbloom who wanted to bring a football team back to Baltimore. That team -- the official Colts franchise -- went 3-9 in 1953. At this point in time, the history of Baltimore football was associated with nothing but losing, and this actual team had gone 5-29-3 over the past three seasons. That's when they hired Ewbank -- on the advice of Browns coach Paul Brown -- who had spent some time in Cleveland and at Brown (where he coached Joe Paterno, the oldest person in the history of the world). Ewbank's team won 3 games against in '54, then 5, 5, 7 and then two straight NFL championships. He did this while playing in the NFL West, the dominant division of the time.
Then he took over the New York Titans, a team that had gone 7-7, 7-7 and 5-9 over their first three seasons, which overstated how good they actually were. In addition to being one of the poorest clubs and on the verge of being insolvent, over the first three seasons of the AFL, only the Raiders
had a worse points differential than the Titans. Then Ewbank rebuilt the Jets the same way he rebuilt the Colts, and five years later, had his team winning the Super Bowl against his old franchise.
Ewbank wasn't an all-time great coach. But his record and his place in history needs to be placed in some perspective. He took two teams teetering on going defunct and made them champions.