Hi Tom No it is not a dumb question.... The faster lens at 2.8  will not be that much sharper than a very good f4, but in order to let in more light the lens has to be bigger and bigger makes them more expensive, but opens up another question in the design like flare.... One of my sharpest tele zooms  I own is the 70-200 f4 L compare the size to the 70-200F2.8, L IS and you can see that the extra size and weigh, sure it can play a part in getting good shots thankfully the 2.8 has Image stabilising and  along with faster optics will allow for better shots as they can be at higher shutter speeds.. 

Designs are improving all the time the latest f4 L in that range has now got IS with a 4 stop range making that  also a great contender.... The final points are,  that in the f4 70-200 the lens is light weight and a simple design so it can be easily hand held, and having less glass kind of makes up for the better design of the faster lens and image stabilising.. Most lens lose quality at the edges of the frame, and on a sensor with 1.5 to 1.6 crop it is also less critical than full frame sensors, and you get more reach with any tele zoom...  (without having to crop)

You can as has been suggested also overcome the lack of speed by pushing up the ISO this however will then make the lens more prone to blown out highlights... (and more dependant on how good the sensor is regarding noise)  I guess after all that, it comes to the law of diminishing returns a Sigma 2.8 300 mmm at 1500 pounds here in the UK would certainly give any of the main makers a run for its money and save you 1500 as well

Danny O'Byrne  http://www.digitalartzone.co.uk/

"All the technique in the world doesn't compensate for the inability to notice" Eliott Erwitt