I think you know this, but your wording could be interpreted as implying that only hardening the tip somehow makes the chisel more flexible. It doesn't. The material property that determines stiffness is Young's modulus, and hardening doesn't change that. As the oft-cited line goes, if it rusts it's 29 Mpsi (in reality there is a small amount of variation based on alloy composition, but you get the idea). A chisel that's hardened along its full length will have the same stiffness as an otherwise equivalent one (same cross-section, alloy, etc) that isn't hardened at all.
Hardening greatly changes the yield strength, but hopefully nobody is bending their chisels *that* much :-).