If some player WANTED to break the consecutive games streak, they easily could with DH in both leagues now.
You'd have to write it into the contract though.
Stolen bases would be next if the game ever returns to that 60s-90s style.
Modern players have flirted w the hit streak, that could fall.
Obviously the records of the dead ball era will never be touched, nor does the modern game allow for the accumulation of career pitching stats, so all those are pretty safe.
Whats so amazing is that Cobb, at .367, representing the complete disaster that baseball is today, with only Luis Arreaz hitting over .300 for his career.