1. Price - the price difference is huge! I have 3 zooms that span the range of 17mm - 200mm.
a. The 24- 105mm f4 L IS USM is currently priced at $1149 (I am using Amazon pricing for comparison purposes).
b. Canon EF 17-40 f4L - $739
c. Canon 70-200mm f4 L IS USM -$1149
The three lenses currently cost a total of $3037
A similar f2.8 would consist of a 16-35 ($1699), 24-70mm ($1898), and the 70-200mm ($2499)
These three lenses currently cost $6096 and ends up costing double the price of the f4 lenses.
2. Weight - the three lens set up weighs about 2.5 pounds less than the 2.8 setup. In addition to weight, you also have more bulkiness and have to spend more on larger filters.
3. The performance of high ISO photography in new cameras. The 5D Mark III is fantastic with high ISOs, so I can get by with F4 in most situations.
4. The size and price of f1.8 primes. When I need to shoot in darker rooms, I usually have an 85mm and 50mm in my bag. The weight together is about 1.3 pounds, provides better low light performance than 2.8 and they don't need to go with me when I just want to shoot with f4. With 2.8, you carry that weight when you won't be shooting wide open.
5. More versatility - the long end of the 17-40 and 24-105 give a lot more usable length than the shorter f2.8 lenses. As an example, the 24-105mm gives you the same wide angle, but zooms out to a usable portrait length. 70mm isn't long enough to use by itself as a walk around lens unless you want generally more unflattering pictures of people. I also find that the difference of 17mm vs 16mm isn't a big deal for me. If 17mm is not wide enough ( which is rare), I can just fire off a couple pics and stitch them together. I messed with the panorama feature on my cameras recently, and even hand held, they came out great. The difference in perspective between 35mm and 40mm is a bigger deal. I often shoot at 40mm and it beats changing out lenses.
The main trade off for f4 is the DOF when compared to f2.8. However, with $3000, I could buy a lot of prime lenses that will produce a creamy DOF and perform even better in low light. As I mentioned, I can choose to leave those home when I won't need them. Also, with a 2.5 pound weight difference, I could carry a few primes and still be carrying less weight. Personally, I only have three primes, the two I mentioned above, and a 100mm f2.8 macro. With this setup, I have a lot of versatility, lower cost, and less weight to carry around. I have no desire to change to f2.8 zooms.