The longer I garden with a permacuture outlook, the more chopping and dropping I do! It does give you slightly less manicured look, but what I love is how it changes my attitude towards
weeds unwanted plants. I can now think "Thanks for harvesting that CO2 from the atmosphere and creating mulch!" If it's a taprooted plant I can think "Thanks for bringing up nutrients from deeper
underground, now I can share them with my favored plants!"
I've been growing comfrey for years, but this summer I've chopped them down (not the main plants, the tall flowering stalks) at least three times, and I think I'll do it at least one more time before they disappear with winter. I planted a mix of cover crops on a huge
berm last fall, and just chopped and dropped them mercilessly through spring and early summer. The soil is now well covered. I'm growing transplants rather than seeds on that berm (tomatoes, winter squash and pumpkin, now some kale and cole crops) and it's working really well.
I would say if you need material for your compost, then you can move it to the compost pile. But if you don't need it, just chop and drop and move on. The best thing about chop'n'drop is how fast you can move with it. Yes, that plant is going to come back. You'll just cut it down again and again. Obviously, this strategy works best in relatively small areas. If you are managing over an acre, you will need some different strategies for some of the space.
I love my Hori hori knife for this work, it's got a serrated edge so I can even mow tufts of heavy grass right at the ground with it (those went into the
chicken nest boxes). My worst invasives are blackberries and perennial morning glory. I still put blackberries into the municipal compost, because I hate getting pricked, but the morning glory vines I rip out and toss into the
chicken pen. During the summer heat the vines wilt and then go brown lying on the ground. When they are crispy I add them to the compost as "brown" material. Once it starts raining I'll still throw them in the pen, they are unlikely to do very well in there and at least will be easy to pull if they take
root (after all the
wood chips and dry leaves that have gone into the chicken pen, the soil is amazing - I'm beginning to harvest it for my gardens, but I still want to build a compost trommel.)