Practicing everything with both hands

Do/did any of you practice everything with both hands leading? I'm relatively new to drumming and I would like to have somewhat equal abilities with both hands. I figure what better way to train my hands than to do everything with both of them. I've been trying to work on the songs, grooves, exercises, etc that my teacher has me doing with both hands. Leading with right and then with left. Hopefully this should be a big benefit to me in the future.

Practicing everything with both hands