This is where having to rinse a filter becomes a problem for me. Unless you rinse the grounds out onto the dirt, your option is to rinse the filter into a trash bag. Now you've got a bag with liquid in it - which is probably fine unless you get even the smallest leak. I'm not put off by leaking coffee, but I don't separate my trash by type, so water in the bag would mix with every other bit if trash...I also like to tread lightly, so carrying less, and creating less garbage is a big plus to me.
Leaving coffee grounds behind isn't "tread lightly", and certainly isn't an option in the places I camp. (Food waste in the desert almost never decomposes - it typically desiccates and hangs around for months or years unless the animals get to it.) Waste and cleanup are actually the biggest reasons I like the Aeropress for camping: I get a nice dry puck of grounds that's easy to knock into my trash bag, and I can usually reuse the paper filter all morning.