Pump rifles have never been very popular. And there are several reasons why. The accuracy potential is actually pretty good. The 7600's use essentially the same barrel as the one used on the 700 and they have always been known for accuracy. The 7600's trigger however is sub-par and there isn't a whole lot that can be done to improve it. You'll likely get more accuracy than a lever action and faster repeat shots so on one level they make some sense. Levers have always been more popular because of nostalgia, but the pumps are a more practical choice if fast firing is important.
I've had one, and my brother played around with one for a few years. After using them I can't think of a single reason to choose one over a bolt gun. All things being equal they are less accurate, less reliable, heavier, and cost more. Their only potential advantage is faster rate of fire. But in the real world that edge is slim to none. Pump action shotguns are pointed, not aimed, and repeat shots can be right with a semi-auto shotgun. Rifles are aimed, not pointed.
You can empty the 4 round magazine by shooting it faster than a bolt gun. But if there is a requirement that all the bullets hit a target I've found less than 1/2 second difference for 3 shots between any of the manually operated actions including pumps, levers, and bolt guns. Semi-auto's are a lot faster in calibers such as 223, but the big game calibers aren't really that much faster for "Aimed" fire. It takes longer to recover from recoil and get back on target than it does to cycle the action on any of them if there is any real recoil.
You also have to consider that if there is any way possible hunters should use some type of rest. Off hand shooting should never be attempted unless there is no other option. When firing from any type of supported position pumps are the slowest to operate.