Personally, I'm a lot faster with my lever guns (.22, 2X 44 mag., 45-70, 12 ga.) than my bolt guns, but, I had never realized that I never use my bolt guns off the bench. I find that bringing the lever back into battery brings me back pretty close on target. It did take a fair bit of shooting to shake the bench-rest bad habits I had picked up since moving to the city. I had completely stopped plinking, and it showed when I started hunting again. Now, I'm almost at the point I want to be at with the levers. I'll have to get back into offhand bolt gun shooting, though.
I don't think I'll ever switch to a bolt gun for quick shooting, just because my bolt guns are longer and clunkier, and I can't see myself buying more guns to do what my lever guns do fanstatically well for me. That being said, my son has a Tikka Battue in 300 WM, and if I had that gun, I would simply put the practice in rather than get a lever gun, having seen what others can do with a bolt gun. In the Battue's case, I might get it ported, because she does move a lot on recoil.
Thanks to the posters who pointed out the bench v. offhand shooting.