And pump rifles are faster than a lever, second to only the semi auto.
I believe that any brit who served in WWII or any person that witnessed them in action would disagree with you. the germans thought that the brits were being issued semis due to the rate of fire that they were able to possess with the proper training. without the proper training, a lever is just as slow as a bolt. to another point, rate of fire is meaningless unless you areable to put all of those shots on target. I could probably drop 5 rounds from a marlin 1895 in 5 seconds if I put my mind to it but I highly doubt many of them would hit what I was aiming at. at the same time I could fire 5 rounds from an AR15 or SKS in 5 seconds and probably still have trouble hitting but much higher precision than the lever.
as for handier, I know I can cover a heck of a lot more distance with a 30-06 than I can a 30-30, 45-70 or 44 mag.