I didn't say it didn't affect peak horse power; I said the area under the horse power curve (total power generated) remains the same whether it is all pilled up at one end with nothing any where else, or a straight horizontal line running from idle to peak RPM (which isn't going to happen either). You can not have your cake and eat it to. So you either have your power evenly distributed, or favoring were you want to use it. On a street driven car that is from idle to about 4,500 RPM, with 90% of engine operation never getting above 3,000 RPM.
If you are racing you want as much of your horsepower as you can get it in the higher RPM range with your foot planted on the floor boards. This is because horsepower is torque applied over time. And the RPM is measured in minutes just like horsepower is. The more RPM's, the more power strokes you can get into a given minute, so you have more power you will have to work with.
Because air is a fluid just like water, it doesn't instantly start flowing the moment you open the valve. It has to build up speed by overcoming inertia and friction. Once flowing it doesn't want to stop either (that annoying physics thing again), and if you shut off a water spigot quickly you get a bang in your pipes, as the water piles up behind the valve increasing the pressure locally creating what is called a water hammer.
Your lumpy idling cam is ground to open the valve sooner than a stock cam, and to keep it open longer than a stock cam, and to close it latter in the compression cycle than a stock cam, just so you can get a column of air flowing into your engine at high engine RPM's. Trouble is at low engine RPM's your valve is open all the time which makes it real hard at low RPM to build compression (the reason a big cam with long duration kills static compression, so you have to have a lot more than a stock piston to run the big cam). In addition to the intake being open with no compression; the exhaust is opening sooner to let the burnt gasses out which is killing the power stroke at low RPM as well. Then there is the rumpity rump sound everyone craves because their hero's race car makes that noise so it must be the source of all of that power. It is caused by overlap. Which is the amount of time during passing through BDC that both valves are open and off there seats so that you have exhaust gasses from an adjacent cylinder which just dumped into the log style manifold pouring into your cylinder that you are trying to empty to get fresh air and gas into. With pressure traveling up the intake path it is even harder to get the air column to start to flow into the cylinder and there certainly isn't a vacuum in the cylinder to suck in the fresh charge. Which is why a big cam sucks at low RPM which is another way of saying driving on the street.
Getting back to the man who "invented" horsepower James Watt; he defines horse power as lifting a 550 pound weight one foot in one second or 33,000 pounds one foot in one minute. He was selling a steam powered water pump to mine owners who had to pump water out of their mines to get at the coal they wanted.
Wikipedia said it best.
"To help sell his steam engines, Watt needed a way of rating their capabilities. The engines were replacing horses, the usual source of industrial power of the day. The typical horse, attached to a mill that ground corn or cut wood, walked a 24 foot diameter (about 75.4 feet circumference) circle. Watt calculated that the horse pulled with a force of 180 pounds, although how he came up with the figure is not known.
Watt observed that a horse typically made 144 trips around the circle in an hour, or about 2.4 per minute. This meant that the horse traveled at a speed of 180.96 feet per minute. Watt rounded off the speed to 181 feet per minute and multiplied that by the 180 pounds of force the horse pulled (181 x 180) and came up with 32,580 ft.-lbs./minute. That was rounded off to 33,000 ft.-lbs./minute, the figure we use today".