As you may or may not know, The founder of the Chicago Bears( my favorite team) was one George Halas. After his stellar career as a College star at Illinios, he was drafted into the Navy during WWI. Rather than going aboard a ship, he was the coach of the all-star navy football team. He was dicharged in 1919 or 1920, and was one of the founding members of the NFL in 1920
What If: Halas was just a average gunners mate on a battleship, and decided to make the Navy his career?
1) would the NFL have been founded?
2)Would Chicago have a pro-football team?
3) Would the team have stayed in Chicago for its whole history?
4)Would pro football be a popular as it is in OTL?
1)Yes the NFL would have been founded. Halas was not heavily involved in the original founding of the NFL, and while the Bears are a charter member I believe it would have existed much the same way it did in OTL without them.
2)Again an easy yes because Chicago really had two NFL teams until 1960. Halas staying the Navy would have most likely meant that the Staleys remain in Decautar, and suffer the same fate as the Dayton Triangles, Canton Bulldogs, Columbus Panhandles, Providence Steam Roller, etc.
The biggest effect is that the team in Chicago would have been the Cardinals. Without having to share Chicago with the Bears, the Cardinals would have remained in one city for the longest of any NFL franchise. Interesting butterflies here because St. Louis was targetted by the AFL in 1960 which is why the league was willing to allow the Cardinals to move to St. Louis. So without the Cardinals in terrible shape in Chicago there probably would have been an AFL franchise in St. Louis. Also likely means that Arizona would have had to wait until the 90's for the possibility of an expansion franchise.
3)Answered this in the above, but yes the Chicago Cardinals would have most likely remained in Chicago. Though the Bidwells might not have become involved since the first experience with football came when Bidwell was involved with the Bears through his connection with Halas.
4)Again I think yes it would remain as popular as it does today. It would lack its greatest rivalary in Bears-Packers, but I don't doubt that football would have progressed much along the same lines as it did OTL.