For the record, all of my coaches told me to choke up with two strikes, every single one from little league to college.
Here's a research article about it. If it's accurate, then coaches should be teaching hitters to choke up on the bat, if they aren't already.
Players using the choke-up grip swing had significant less swing time and stride time than the normal grip swing. Results also indicated significant greater bat velocities (p = 0.01) with normal grip swings than the choke-up grip swings. In addition, further results indicated no significant differences (p = .90) between choke-up and normal grips in bat-ball accuracy. These findings suggest that the choke-up grip facilitates faster swing time and stride time without compromising bat velocity or contact accuracy.