I don't think you'll find a single person, including Rose, as conceited as he is, who claims Rose was a better hitter than Cobb. He just has more hits. There is pride in that.
For that matter, I don't think there will ever be another player who finishes within 30 points of Cobb in career BA. The closest active player is Pujols at .325. The most recent player to even sniff would be Tony Gwynn (think of how many times you've seen him on base), and he finished at .338.
BA just isn't as important anymore. You would think with a league twice the size it was when Cobb was playing, the elite hitters would take advantage of the awful pitchers and put up crazy numbers for average, but it hasn't happened.