Yes, all good points! There are quite a few edible weeds I am happy to encourage. Purslane, hoary cress, salsify, and yellow dock are all great, for example. The quackgrass and johnson grass are fine, too – the seed heads are nonbothersome when I step on them, so they’re a perfectly fine ground cover.
The foxtail grass, I want out. Also the other species of grass that has even nastier, pricklier seed heads. And the prickly lettuce (which I know can be used as a painkiller, but it’s definitely poisonous, and invasive, and it will cross with my edible lettuces, and those thorns are horrendous). And those goatheads are beyond unwelcome. Thorns and burrs aren’t welcome, period.
I might permit some edible grasses with poky seed heads to live in a corner of my yard where it isn’t meant to be stepped on as a groundcover. Wheat, rye, and so forth. Those seem to grow wild in our state, and they’re fine as long as I’m eating the seed heads and not getting them stuck to my socks.
Meanwhile, can you think of any value in bindweed? 
That’s by far the biggest invasive I have to deal with right now. It’s not nearly as big a deal as, say, burr grass or goatheads; it’s quite pretty and harmless. It’s just that it’s so invasive that I want to get rid of it because there seems to be no way to keep it in balance when it’s around.