Ty Cobb missed the last month of the 1918 season...because there was no last month in 1918, as MLB closed the regular season around Labor Day due to World War I. Cobb then served in the military, but Germany's surrender on November 11, 1918 allowed Cobb to resume his baseball career the following spring. The shortened 1918 season probably cost Cobb between 30 and 50 hits.
Another advantage Pete Rose had over his likely competitors in achieving the career hits mark is that for most of his career Pete batted leadoff and, while Rose had decent mid-range HR power in his prime years between 1965 and 1971, usually getting 10 to 16 HRs a season, after 1971 Pete only reached double figures in HR once. While he did draw some walks, with a powerful lineup behind him and batting leadoff, Rose was in a perfect position for teams to pitch to him rather than around him.
Someone such as Trout, with more power than Rose ever had, is a player I would expect pitchers to be less likely to just throw strikes to, and is also a hitter I would expect to bat second and third in the lineup much more often than Rose ever did, especially as he ages. He probably will not rack up as many plate appearances, year in and year out, as Rose did.