Agreed on this! But, not a bad idea to explore alternatives. I've been a triathlete for 12 years and have put in better than 10,000 miles on a bunch of different continents, and have never found a situation where carrying a firearm while running seemed appealing. The biggest weapon you have for self defense while running, like anywhere else, is situational awareness- always assess your surroundings, and if you think you might be in a bad spot, use your mobility to get out of it.
Regarding carry, the only thing I've ever taken is mace. I don't even carry an Ipod anymore while running because they get so gross and die so quickly with sweat... there is just not a chance I'm carrying a holster and a firearm. A small canister of mace, however, will handle almost all threats you can reasonably expect to defend yourself from while winded, alone, in the open and away from where you live. The only problems I've ever had have been with dogs, which circles back to the point about SA.