really long time, which gives him additional opportunity to accumulate WAR even though he might not have been great in his prime.

Rose was a singles and doubles hitter (in his prime he hit a good number of doubles, but not over the course of his whole career), he never had any real power. He only had a slugging % over .470 once, and his career slugging was barely above .400 (which is downright bad). He walked in less than 10% of his plate appearances, which is bad, so despite a ton of singles his career OBP is good but certainly not great. He was also a liability on the bases. He was a very good player, but you're ignoring the fact that he had pretty empty batting averages and having a bunch of singles and a few doubles, while playing forever to increase his hit count, doesn't make him an all-time great.