So, after grumbling about it, I went ahead and ordered the cheapest of the tea-makers from
this post, the Sunbeam HTM3 Tea Drop. It arrived today, so I've been playing with it.
Obvious drawback: it doesn't have a real steeping system; it drops almost-but-not-quite boiling water on the tea fast enough that it doesn't immediately drain away, so the tea is immersed in the hot water, but not for long enough to really steep, since the water is slowly draining away and being replenished throughout the process. This means it's not really suited for whole-leaf teas at all. And, as noted, the water isn't quite boiling, so it's not going to extract all the flavor from black tea, although it's hot enough for green.
Still, I'm not a big-time tea snob; I'm more an indiscriminate collector of teas. (Hey, it works for the Spouse and Transformers.) An awful lot of what I have and like is flavored crap rather than serious whole-leaf teas. So I was thinking that perhaps this will work out anyway, at least for said flavored crap - obviously I'll continue to steep a first-flush Darjeeling or a Ti Kuan Yin oolong properly, with boiling water just off the stove.
So, after running it once with plain water to clean the system from any dust accumulated in shipping, I tried it with a very strongly flavored black tea, Celestial Seasonings' Nutcracker Sweet (seeing as how I still have some from last holiday season, and it's not my favorite, so if it's awful, I won't care that much.)
Water: 24 oz., to make two 12 oz. mugs
Tea: 2 teabags Nutcracker Sweet (one on each side of the brewing basket)
Setting: as far on the "strong" side as the knob goes
Observations: the lack of steeping didn't change the characteristic cinnamon-candy scent of the flavored tea at all; it was highly aromatic all through the brewing process. The tea started very light, almost clear; darkened over the brewing time; and ended up light again. In the carafe, it had good, deep color and smelled like I expect this tea to smell. The brew cycle was over in about 5 minutes.
Flavor: Somewhat weak compared to my usual 5-minute steep, but still had decent tea flavor as well as the cinammon-candy flavor - probably the equivalent of a 3 1/2-minute steep, without some of the darkest notes. The machine kept the carafe quite warm; the second cup was not noticeably cooler than the first one, despite being 30 minutes later. (Also, apparently the teacup I was using holds closer to 10 oz. than 12, as I ended up with two and a half cups.)
Conclusion: a partial success. With some tinkering, probably involving adding more tea leaves, this gadget can probably be coaxed into making perfectly drinkable tea, and before 11 am, I'm unlikely to be drinking something nuanced enough for this thing's flaws to be terribly glaring. It won't make high tea, but it'll make serviceable jumpjuice.
Next experiments: (1) Republic of Tea's bagged (i.e., not whole-leaf) flavored green tea, and (2) Twinings English and/or Irish Breakfast loose tea.