Any type of immersion brew benefits from immediate agitation in my experience, aeropress and french press (which gets aggressively swirled under my hot water tank while it's filling.) You can aggressively stir aeropress as well, you just need to manage it dripping from the bottom using more filters, finer grind, invert method, etc.
You still have to screw a lid on it, how is it any easier than simply screwing on a different lid? Or perhaps you meant “cheaper” instead of “easier”. :-)
