There was no national champion in 1924. Nor at any time during the 20’s and early 30’s. Notre Dame was retroactively voted #1 in 1924. And Rockne led the charge to have them named national champions some time later. I cant remember the exact timeframe however. I dont know anything much about football from that timeframe and the Irish may veru well have been the best team that year. But those on this board that argue over 1973 or 1966 or whatever year should know that their Irish claim retroactive titles no different than any other school. One could probably make arguments about 1943 as well. But to me it is really more of a waste of time. Enjoy what you have in the moment and realize it may be years before you ever see another one. If you are even lucky then. The rest is nothing more than bragging rights about a school or program that really doesn’t mean much anyway.
You're correct about 1924 with Rockne, before he died in 1930, asking Frank Dickinson who had a mathematical system for selecting a NC, evaluate. Dickinson selected ND based on his formula, using SoS. Thirty points for beating a strong team, 20 points for beating a weaker team. The only other unbeaten team in 1924 was Stanford (considered #2), who lost to ND in the Rose Bowl. Easy for Dickinson, the NCAA and any other major selector retrospectively.
I was curious about Bama's claims to 1930 and 1934, which I mentioned to Bishop.
In 1934, Minnesota was widely regarded as the best team that year, reflected in the inaugural AP poll (they then skipped 1935 and are continuous from 1936). Minnesota finished way ahead (635 pts, 50 first place votes) to #2 Stanford (468 pts, 8 1/2 first place votes) and #3 Alabama (438 pts, 5 1/2 first place votes). Alabama did not play anyone in the regular season that was ranked in the final AP poll. Minn did not go to a bowl. Minn. beat #4 Pittsburgh. Bama beat #2 Stanford in the Rose Bowl. The NCAA recognizes Minn as NC.
In 1930, it really comes down to Notre Dame and Alabama. Wash St was undefeated and Michigan had no losses but a tie. In the regular season, ND beat Northwestern (#4), USC (#6), and Army (#9). Alabama beat #10 Tennessee. (Dickinson rankings) The ND team received a ticker tape parade in Chicago on returning home after beating USC. Alabama beat Wash St, previously unbeaten, soundly in the Rose Bowl. ND did not go to a bowl. This is considered Rockne's greatest team and Wallace Wade's greatest team. From what I can tell, popular opinion was fairly overwhelming that ND was the best team that year and certainly by SoS.
I'd say Alabama is regarded as the 1925 national championship team and recognized as so by the NCAA and major selectors. In 1926 the NCAA has a tie between Alabama and Stanford. Bama had good teams through the rest of the rest of the '20s, '30s, '40s and '50s with the NC drought ending in '61.
As you say, perhaps we pay too much attention to it and the numbers on the helmet. Those clearly do not bear a lot of scrutiny of the history.