I think what makes it so magical is that it's airtight and so the pressure inside goes up when you brew it, also most French presses I have used have just a steel mesh instead of a coffee filter so you get silt in it.
I heat one cup of water at a time in a small stove pan. It's quicker for one cup than drip. It tastes a bit like espresso, but not quite as strong. Similar to cold brew in that it doesn't taste "acid-y" (like from when you heat the coffee pot to long), and is pretty smooth.