In the 1960s the Redskins weren't bad at least starting around 1964 when they traded quarterback Norm Snead to Philadelphia for future Hall of Famer Sonny Jurgenson. They also picked up tailback/receiver Charlie Taylor who would also end up in the Hall of Fame and you could make a good case that he's the best WR of his era and of all time. And they picked up TB/WR Bobby Mitchell in 1962, who's also in the Hall of Fame. Drafted tight end Jerry Smith who should also be in the Hall of Fame. Drafted linebacker Chris Hamburger who just went in to the Hall of Fame. Hall of Fame LB Sam Huff was still there.
The Redskins weren't bad in the 1960s, but they weren't very good either, they only had one winning season, 1969 Vince Lombardi's only season in Washington and had several 7-7 seasons and a few 6-8 seasons, but they were building a lot of the success that the Redskins had in the 1970s started in the 1960s with the players that they drafted, including tailback Larry Brown in 1969 the Redskins first 1000 yard rusher. The Redskins had some of the best passing offenses in the NFL in the 1960s from 1964 and on, but they never had a solid running game until 1969 with Larry Brown.
But they also had some of the worst defenses in this decade unlike the 1970s and 80s when they were always in the top 10 in defense with George Allen and then Joe Gibbs where they win five NFC Finals from 1972-91 and three Super Bowls in that same period. Which is why Vince Lombardi and George Allen were so important for the Redskins to change the culture in how they operated.
When George Allen took over the Redskins in 1971 as head coach/general manager, I believe he knew he had a good nucleus, but that he had to add to it to make the Redskins a winner and contender. Which is what he did, he did not come to Washington from Los Angeles, where he was one game away from the Super Bowl a few times to have a 500 team or a team that barely has a winning record, but he wanted to build a champion win the NFC East, the NFC Final and the Super Bowl. He had very good teams with the Rams that always had one of the best defenses which was his background. He was George Halas's defensive coordinator with (da Bears) before he went to Los Angeles to be the Rams head coach.
His philosophy was simple. Tough take charge defense that takes away the run to attack the QB. Run the ball on offense, protect the QB and take a few shots down field on offense off of play-action and win the turnover battle. That if you do these things well you'll win much more than you lose and when he came to Washington that's what he wanted to establish. He knew he had a good group that he had to add a few pieces to make them winners and contenders,which is why he brought in some Rams, like defensive tackle Diron Talbert who reminds me a little of DT Dave Butz who Allen also brought to Washington. As well as linebacker Jack Pardee who would later be the Redskins head coach from 1978-80 and others.
The Redskins in the George Allen era were nicknamed the "Over the Hill Gang", not because his players couldn't play anymore, but because most of them were in their thirty's when they got there. Or were going bald or were coming from teams, like QB Billy Kilmer's case that no longer wanted them and when you get released from the New Orleans Saints like Kilmer did in 1971 you are starting over and trying to find a place for yourself. Because the Saints were awful their first few years, but it all worked for Allen in Washington because he sold them on the idea that they are here to win. "Thats why I brought you here and kept you here to win and become champions". Something a lot of these players had never done before.