Both my rifles have a very crisp c31/2 to 4lb trigger pull, but also have a push forward set trigger, where the pull weight is much lower. I find that using the set trigger makes it more difficult to shoot well. I was taught to shoot by squeezing and squeezing the rifle firmly to control the recoil at the same time as squeezing the trigger. With a light trigger I find the rifle fires before I am ready and I cannot control the recoil and rifle jumps about. I also dislocated my left wrist (I shoot left handed) several years ago, and whilst I have plenty of control I don't have really fine sensitivity in my left fingers, especially when cold.
Would welcome any body else's thoughts on the matter, especially those who use light trigger pulls. I suggest no right or wrong answer, just what works for you.