I forgot about iced tea, but I'm under the impression that how popular it is depends on the region of the US you're talking about. I don't see a lot of people drinking iced tea in my area, and I don't think I've ever seen anyone make it for themselves.
Sweet tea is quite regional (the South).
Iced tea's popular in much of the country, but I think making it at home has dropped off just like making many other things at home has (how many people make their own stock or broth anymore?). These days, a gallon of store-brand iced tea is just about the cheapest drink most grocery stores stock—barely more expensive than making it at home, really, so why bother?
Old-school restaurants, and especially diners, may have a mid-sized glass jar[0] of sugar with a metal lid and little metal flap on it (that flips up if you tip it, allowing some sugar out) left on the table, mainly used to sweeten coffee and iced tea. This is getting less common, in favor of little trays of sweetener packets, but you still see it sometimes. Used to be very common, 1990s and earlier.
True sweet tea (huge in the South, i.e. the part of the country that seceded during the Civil War, but much less ubiquitous outside it) is incredibly unhealthy. It contains more dissolved sugar than is easily achievable in room-temp-or-lower water/tea, by adding it during the boil, same as how you can super-concentrate sugar in water when making simple syrup (though it doesn't go that far) and it retains that sugar even when it's refrigerated. Sweetened iced tea has a much broader range of sugar levels, and may be relatively healthy, with only a little sugar, or very sugary.
Outside of the South, you'll often get sweetened iced tea if you ask for "sweet tea". It's fairly uncommon to see the real thing in Northern or Western restaurants. This sometimes leads to confusion, with non-Southerners going to the South and ordering sweet tea and getting something offensively sweet compared to what they're used to, or Southerners ordering it elsewhere and being disappointed with what they're served.
[0] Diner-syle sugar pourer: https://img1.etsystatic.com/040/0/6766475/il_570xN.635748831...
Note: this does not apply to bottled/canned teas, which are usually close to "half and half" in sweetness.
Most restaurants here serve soft drinks from a fountain rather than individual cans/bottles, so refills are free. If a restaurant uses individual containers for service, you will have to pay for refills. However, iced tea has free refills everywhere I've ever seen.
For my part, despite working at it for years, I still don't really like cheap tea (the stuff I could actually afford to drink every day, and that can be found without seeking out rare-in-the-US tea shops or ordering online), though higher-end tea is really good.
We drink a ton of iced tea, but that's easily made on the stovetop in a large pot, and can be bought in gallon-quantities at the grocery store. Having a kettle doesn't improve iced-tea-making very much.
[EDIT] Part of it may be that we drink on-the-go more than other countries. Just a guess, but might be true. Iced tea and coffee (hot or cold) are both much better for that than hot tea—one doesn't usually make a thermos-full of hot tea and drink it straight from the thermos, I'd expect (but maybe I'm wrong?) but that's normal for coffee.