I use a pretty coarse grind in my toddy maker, but it has a rubber plug in the bottom and you let the slurry sit overnight and then pull the plug. But I'm with you; I don't particularly care for cold brewed coffee. Tastes "swampy" to me. I'd much rather have an iced coffee made with an Aeropress.
I feel the same about "sun tea". It takes heat to extract the deeper flavor compounds in both. A friend gave me one of
these for Xmas a long time ago because I'd been telling her how grandma used to make cold-brewed coffee. I tried it a few times and decided it wasn't for me.
On the positive side: This thread has triggered me & Mrs T to go through my junk to clear out some the stuff I'll never use and call a charity to come pick it all up. Let's see: coffee toddy: check, Mr Coffee: check, Bodum electric vac pot: check, a handful of press pots: check, whirly blade grinder by the basket full: check, Baratza Maestro: check, and the list goes on. It ought to make a nice deduction when I do taxes next April!