Here’s what happened to Hornsby, as best I can figure out from various written sources and some conversation with the old STL sportswriter Bob Broeg:
Before 1918, the Cardinals, a poor team then, had an infield that was not a settled thing at all, with people moving around a lot, so it’s sometimes hard to tell who could actually play where. Hornsby took over the shortstop job because he was the best SS among all these infielders. However, in 1918, Hornsby, whose arm had been OK for shortstop before, hurt the thing, missing a few games, and his shortstop defense dropped quite a bit. Then, in 1919, Branch Rickey took over the Cards and moved to improve the infield. He brought in Doc Lavan, a good glove no hit shortstop, in his prime at age 28, that Rickey had managed earlier with the Browns, and Milt Stock, a young, good hit poor field infielder who had an arm but absolutely was not a shortstop. Lavan took over the shortstop job and Stock took third base because his arm was better than the injured Hornsby’s. You can argue that Hornsby, weak arm and all, was a better third baseman than Stock, but Stock had the better arm, so the assignment of positions was just simple logic. Hornsby’s arm never recovered and then he had the inner ear thing in 1923 that made him unable to go back for fly balls. - Brock Hanke