Sorry, I was a touch unclear in my original post. The problem isn't that the product has little or no value-add, it's that for the population of tea enthusiasts, it has actually negative value.
The tea enthusiast community is as much about tea accessories - infusers, cups, mugs, kettles, pots, sharing pitchers, tea pets, gongfu tray, etc. - as it is about the tea itself. For the sort of folks who are happy to drop dollars on tea goods, a machine built around excluding 90% of the fun actively goes against the grain. In addition, for $1000 you can buy several of the really, really nice tea pots that make most tea enthusiasts drool.
Please, don't take my word for it. Check out any popular tea blog. Or the agenda for any industry conference.
The way I see it, tea drinkers are likely to fall into a matrix of degree of tea enthusiasm, degree of tea accessory enthusiasm, and price insensitivity - let's call it a 3x3x3. 0 indicates some small degree of enjoyment or price insensitivity.
Most tea drinkers by numbers are going to be found in Tea[0]Accessory[0]Price[0] - folks who drop a lipton bag in their daily cup. They aren't likely to shift from their 1-cent tastes-like-tuchus tea to a $1000 machine with several-dollars-per-serving tea. If they cared that much they'd either not drink lipton, or if they were that price insensitive they'd at least buy better tea bags.
The second largest group is Tea[1]Accessories[0]Price[0]. These folks shell out for nicer tea bags, with tea comprised of tiny remnants of leaves rather than out-and-out fannings. They like tea; they think of themselves as tea drinkers. They may have a favored tea pot. They may know what whole leaf tea is and buy it on occasion. Their tea still only costs about 20 cents per cup (something like Vahdam) down to 6 cents a cup (PG Tips, the tea that every English hospital sends you home with after giving birth. And... it's surprisingly pleasant.) There is, again, a pretty steep difference between "I throw a better tea bag into my coffee cup for 6 cents rather than a shit bag for 1 cent" and "I will shell out a thousand bucks for a machine that will let me pay starbucks prices for a cup of tea."
So, addressable market is pretty tiny. Let's jump over to Price[2]. It exists. For tea enthusiasts most will be found in something like Tea[2]Accessories[2]Price[1]. Tea, it should be noted, is a cheap pass time. Even very fine tea is not generally expensive. Even very fine tea pots will not generally break $200. For these folks, there is pleasure in discovering new tea, buying new teaware, pairing teaware to tea (e.g., the right heat-conserving properties of pot to the leaf), and so on. Commoditizing their tea actively deprives them of pleasure. Removing tea-making accessories from the process deprives them of pleasure. It's like trying to sell k-cups to that guy who makes a big deal about this new single-farm roast from Nicaragua that he found for his pour-over, that he likes to make on his artisanal aeropress rig he backed on kickstarter. And where do they fall on price? I'm pretty price-insensitive on tea; I regularly buy the good stuff. On the higher end (let's not talk about seriously aged pu'erh), for instance, I got this spring's Ai Jiao Rock Oolong Tea of Wu Yi Shan, which ran 9 bucks USD for 50g. That's good for about 18 8-ounce cups - or lets be fair, about two weeks of my big morning cup (though that nice oolong is hardly a daily drinker). That puts me at 64 cents per cup. My daily drinker is an earl grey supreme w/ silver tips from Harney & Sons, which runs 25 cents for my big morning cup.
So which market segment are they looking for? To care about tea, but not enough to care about commoditized tea servings. To not care about accessories. And to not care about a hundred-fold price increase up front and a ten-to-hundred-fold increase per cup. So... tea[1]accessories[0]price[2+]?
I can't say it doesn't exist, but as addressable markets go, there's no reason to believe it's anything but vanishingly tiny. Which, really, anyone in the tea enthusiast community could have shared with them right up front.
That's not to say there aren't things that are in-demand in the tea community. They're just not the sort of things VCs would throw money at.