The board was originally a bunch of local supporters of the team. As football became more of a business in the 30s and 40s, the board got more involved such as setting Curly's salary, approving budgets, etc. Since there was no owner, it was a necessary process back then. After forcing Curly out, the board made some bad hires in Ronzini, Blackburn, and especially Scooter. They also missed the boat on Tom Landry, but Lombardi ended up being a good consolation prize!
To their credit, the board kept reorganizing and trimming down to be more effective in the 1950s. Prior to that there were factions within the board that wielded their influence to effect changes. The coaches used to have to give weekly reports to the board after games. When Lombardi was hired, even though the board had been streamlined around the same time, he still laid down the law and told them that
he was running the team, not them. Lombardi hand-picked Bengston to be his successor but then left for Washington. The board re-took control and forced Bengston out in order to hire Dan Devine, Bart Starr, and Forrest Gregg successively. During all of this time, you had two very influential presidents in Olejniczak and Parins from the late 50s to the late 80s. However, IMO it wasn't until Bob Harlan rose through the ranks that we had a truly
effective president at the helm. He boldly fired Tom Braatz (mid-season I think) and hired Ron Wolf to be the GM. In turn, Wolf hired Holmgren and the next 30 years of prosperity is now a part of his legacy. It seems to me that Harlan consolidated control of football operations in the role of the president.
Ironically, there was just an article about Mark Murphy's 3 year retirement plan:
https://profootballtalk.nbcsports.com/2022/07/03/mark-murphy-confirms-retirement-plan-for-2025/