I can agree with some of what you say above-- but baseball WAS a national sport for virtually ALL of the 20th Century-- Babe Ruth was FAR and away the biggest sports personality in America for ~15+ years-- as were the Yankees the biggest sports team (once Ruth made them into a dynasty)-- people ALL OVER the US loved or HATED the Yankees... Boxers (like Jack Dempsey and Joe Louis) were the clear top challengers to baseball's hegemony-- with (ironically) top racehorses (like Man o' War, War Admiral, and Seabiscuit) being next in the pantheon of national sports figures...In the 1890's, there wasn't really much "national sporting news." Sports were still very regional. The only way for people to travel long distances was by train. It was a big deal for Ohio State to play Minnesota or Wisconsin.
Baseball is still the perfect sport for radio. The sport is slow enough that you can describe everything on the radio. Television made us realize how slow the game is, which is why it's less popular now. Baseball's peak popularity was in the days of radio.
Most early football history took place in Pennsylvania and Ohio. Of course, some of the Ivy League schools are also a part of football history. It's not really an accident that the most-contested college-football rivalry is Lafayette and Lehigh (both in eastern Pennsylvania).
But, the bottom line is that there MOST DEFINITELY were NATIONAL sports figures, and national sports-- and football was NOT among the top three in importance at that time-- some people cared about college football (remember, in those days, less than 10% of Americans went to college)-- but pro football was nowhere close to being an important, widely covered sport. The top football athletes (based on fame) were in college (e.g.- Red Grange)-- and lost any prominence, once they graduated-- often, they did not bother to even play pro football.