Too many threads on this (and certainly other) forums about defective accelerator pumps causing everything from acne to nuclear fission!
The accelerator pump in a carburetor is a CONVENIENCE, NOT A NECESSITY!
Most engines, excepting those where a power valve is in the bottom of the accelerator pump well, will run at wide open throttle with the accelerator pump completely removed from the carburetor. This practice was quite common, at least in rural areas, during WWII with gasoline rationing.
The main function of the accelerator pump is to furnish some fuel to transition from the off-idle circuit (NOT THE IDLE CIRCUIT) to the main metering circuit when the operator wishes to go immediately from idle to wide open throttle.
If one is not in a hurry, one can feather the accelerator pedal (assuming the idle is properly adjusted) and accelerate the engine. Just more slowly up to some RPM, which will be different for each class of engine. Above this threshold RPM, the accelerator pump does nothing, regardless of the dynamic speed of RPM change.
Do accelerator pumps go bad? Certainly, but generally over decades (neopreme pumps used in ethanol fuel are an exception, and can fail very quickly). The two carbs on my shop truck are approaching 22 years of service without being touched (no new pumps, no new adjustments). The single carb on my hot rod has been in place untouched now for about 10 years; again, no new accelerator pump, no adjustment.
So why does an engine bog from idle?
Assuming the engine still has its original ignition system (if not, consult an electronics engineer):
(A) most common cause is the idle is set TOO RICH!
(B) second most common cause is a defective advance mechanism in/on the distributor
(C) then we have valve springs, and other causes.
Explaining "A" above.
Most carburetors have TWO idle ports per primary throttle. So a one barrel would have two, a two barrel would have four, and a four barrel would also have four. There are exceptions, but this is most common. Since most here are dealing with a six cylinder, we have two idle ports. One is called the lower idle port, generally is round, and generally has the idle mixture volume screw sticking either into or close to the port. This port is below (engine side) of the throttle butterfly. The other idle port has a variety of names, most commonly called the off-idle port or the idle transition port, or the idle transition slot. Generally, this is a vertical slot beginning at approximately the center of the throttle butterfly when closed, and open for a distance upward from the beginning point.
For really good performance with most carburetors (again, there are exceptions), a good rule of thumb would be 65 percent of the volume of idle fuel being supplied by the lower idle port, and 35 percent supplied by the idle transition port. To achieve this balance, the throttle butterfly MUST be slightly open at idle to expose the idle transition slot to the air stream. Many enthusiasts set the idle with a vacuum gauge (correct for carburetors with an air-bled idle, but not correct for most single barrels that will be found on Chevrolet sixes). If the enthusiast sets the idle for the highest vacuum; at what throttle condition is set? Vacuum is measured to the engine side of the throttle plate, so highest idle vacuum will be acquired when the throttle butterfly is completely closed. How does this effect the idle fuel flow? With the throttle completely closed, the idle transition port is covered and provides zero fuel, and 100 percent of the volume of idle fuel comes through the lower idle port. But more importantly, there is virtually no air velocity in the intake runners, which creates "puddling", a condition where droplets of fuel adhere to the walls of the intake manifold. Now, the operator opens the throttle. The sudden inrush of air into the intake runners sweep the droplets into the cylinders, creating an instantaneous over-rich condition, and a hesitation. But the idle transition slot had no fuel flowing, so there is no inertial flow of fuel BEFORE the accelerator pump fuel arrives and there is an instantaneous fuel starvation, and the hesitation becomes a bog, or even a stall.
So before throwing rocks at the carburetor, and its accelerator pump; test the pump! (A) start the engine, (B) stop the engine ("A" and "B" are necessary to assure that there is actually fuel in the carburetor, modern fuel can evaporate overnight), (C) remove the air cleaner, (D) put on a pair of goggles, (E) open the choke butterfly, (F) look into the top of the carburetor from a respectful distance, (G) rapidly move the throttle arm from the idle position to the wide open position. You will either: (H) see a stream of fuel - the pump is good, or (I) see no stream of fuel - the pump should be replaced.
Once you have determined that the accelerator pump is functional, find the real problem!
And should you disregard ALL of the above, and are totally convinced without testing, that your accelerator pump should be replaced.................................I know a guy that sells carburetor kits!!!!

Jon.