I think the reason it's hard to find sweet tea at WDW, is because of the huge volume of people going through the restaurants, they'd almost have to have people whose only job is to brew fresh sweet tea all day long.
I think the only way Disney could offer fresh sweet tea, would be to have a sweet tea vat/drum, similar to the "Hurricane" specialty drink vat/drum in the CityWalk utilodor tunnel underneath Pat O'Brien's. The only problem is Disney would have to have one at every restaurant, which definitely wouldn't be cost effective.
Outside of WDW, in Orlando, you can find sweet tea at CiCi's Pizza, and Golden Corral Buffet & Grill (both have locations very close to DTD).
I'm pretty sure that some different places use a fructose syrup to sweeten when they to make large quantities of fresh drinks such as sweet tea, punch, and lemonade.